To get all of them for the expansions up to, one can use ( in addition to the basic cases already given ) the recursion relation

In addition, concessions were granted for expansions to the network: the A3 would extend the north-south highway from Porto up to the Spanish border, the A4 would reach east from Porto to the city of Amarante, and the A5 was to reach from Lisbon about west to the coast.

The key schedule, however, is more complex, expanding the key using an essentially one-way function with the binary expansions of both e and the golden ratio as sources of " nothing up my sleeve numbers ".

For the 1998 installation, WaterFire expanded to include 81 fires, with expansions up the Moshassuck River and into the basin at WaterPlace Park.

With the completion of all planned expansions, this can be expanded to handle up to per year.

The games on normal N64 cartridges could also hook up with DD expansions, for extra levels, minigames, even saving personal data.

He gave up making welded-metal sculpture in 1966 and organised a series of Happenings from 1967-1970, in which he produced expansions in the presence of an audience.

Full-size keyboards, speech synthesizers, sound generators, disk drives, and memory expansions ( up to 64K ) were a few of the options available.

I therefore decided to split up the fall in pressure of the steam into small fractional expansions over a large number of turbines in series, so that the velocity of the steam nowhere should be great ... I was also anxious to avoid the well-known cutting action on metal of steam at high velocity.

Renovations and expansions are installed to the hippodrome, telephonelines are set up, the sales of yearlings see historic highs, and one can count up to 62 English and French yachts in the basin.

In 1943 there was a Battalion of American Seabees, the US Construction Corps, living on a merchant vessel tied up in Penarth docks, while they built a large number of Quonset huts for the rapid temporary expansions of Llandough Hospital and Sully Hospital.

In 1943 there was a Battalion of American Seabees, the US Construction Corps, living on a merchant vessel tied up in Penarth docks, while they built a large number of Quonset huts for a rapid temporary expansions of Sully Hospital needed for the extra wartime pressure of additional patients, both military and civilian.

In 2008, it was announced that a study to review necessary expansions and modifications was completed, and a masterplan was written up soon after.

The buildings previously made up Glenmore Elementary School, but have since seen several expansions and improvements, including a full-size grass field, and a new wing which houses the gymnasium, the Lecture Theatre, and the Senior School.

One of the first expansions was the acquisition of the Aroostook River Railroad which had built up the south bank of the Aroostook River from its connection with the NBR at Aroostook, New Brunswick to Caribou, Maine.

It was released on November 14, 2001 with overall positive reviews thanks to the addition of a downtown area outside the neighborhood, which became the set up for upcoming expansions packs in which new areas were added ; it also served as the inspiration for The Sims 2: Nightlife.

He analyzes the expansions of the cumulants of up to the term and shows that the following choices of produce reasonable results:

Further expansions of both Carolina Forest Boulevard and River Oaks Drive ( creating an loop ) would open up to development west of the Intracoastal Waterway.

Notice that the entire right diagonal of Pascal's triangle corresponds to the coefficient of y < sup > n </ sup > in these binomial expansions, while the next diagonal corresponds to the coefficient of xy < sup > n − 1 </ sup > and so on.

These relations are a direct consequence of the basic properties of determinants: evaluation of the ( i, j ) entry of the matrix product on the left gives the expansion by column j of the determinant of the matrix obtained from M by replacing column i by a copy of column j, which is if and zero otherwise ; the matrix product on the right is similar, but for expansions by rows.

His first initial expansions moved Harris Teeter into Nashville, Tennessee, Atlanta, Georgia and Jacksonville, Florida which happened right after his take-over as president, through the end of the 1990's.

That development, in turn, formed the foundation of still more significant expansions in later years -- in gear cutting, in circular graduating, in index drilling, and in many other fields where accuracy was a paramount requirement.

The original proof is based on the Taylor series expansions of the exponential function e < sup > z </ sup > ( where z is a complex number ) and of sin x and cos x for real numbers x ( see below ).

: The scroll shares all the major typological features with the SP, including all the major expansions of that tradition where it is extant ( twelve ), with the single exception of the new tenth commandment inserted in Exodus 20 from Deuteronomy 11 and 27 regarding the altar on Mount Gerizim.

Although originally applied only in quantum field theory, such diagrams now find increasing use in any area where perturbative expansions are studied.

All Command & Conquer real-time strategy games except Command & Conquer: Generals and its expansions have featured the " side bar " for navigation and control as opposed to many other similar games where the control bar is located on the bottom of the screen.

This allowed hybridization with the Black-headed Grosbeak subspecies P. melanocephalus papago Range expansions also seem also to have occurred elsewhere, for example in northern Ohio where it bred rarely if at all in the 1900s ( decade ), but it by no means an uncommon breeder today.

For instance, C macros, where macro expansions may result in common subexpressions not apparent in the original source code.

Recent expansions and relocation in the UFL have shown a preference for media markets where the National Football League does not operate a team.

The resulting orthography is seen by some as confusing and unsightly, particularly if it is the second character that is written in kana – the kana characters are where okurigana would be expected to go – and this is one motivation for expansions of kanji lists.

Gimbutas believed that the expansions of the Kurgan culture were a series of essentially hostile, military incursions where a new warrior culture imposed itself on the peaceful, matriarchal cultures of " Old Europe ", replacing it with a patriarchal warrior society, a process visible in the appearance of fortified settlements and hillforts and the graves of warrior-chieftains:

This is true to a slight extent in the epigyne of Trabeops, but more markedly so in that of many species of Geolycosa, where the lateral expansions often conceal the openings of the spermathecae, as in the epigyne of Geolycosa pikei.

Multipole expansions are very frequently used in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region.

Bassinets and equipment are arranged in six-unit pods where there is a noticeable reduction in the bright lights and noise levels ( current expansions are planned which will convert existing pods to private rooms ).

Beginning around 1999, Sivers oversaw expansions of his roster with such collaborations as the one with Oasis Disc Manufacturing President Micah Solomon, where Sivers partnered with Oasis Disc Manufacturing to distribute the complete Oasis artist roster at the CD Baby store ( an arrangement still valid currently ).

Sargon has often been cited as the first ruler of a combined empire of Akkad and Sumer, although more recently discovered data suggests there had been Sumerian expansions under previous kings, including Lugal-Anne-Mundu of Adab, Eannatum of Lagash, and Lugal-Zage-Si.

The first, termed Proto-Isaiah ( chapters 1 – 39 ), contains the words of the 8th-century BCE prophet with 7th-century BCE expansions ; the second, Deutero-Isaiah ( chapters 40 – 55 ), is the work of a 6th-century BCE author writing near the end of the Babylonian captivity ; and the third, the poetic Trito-Isaiah ( chapters 56 – 66 ), was composed in Jerusalem shortly after the return from exile, probably by multiple authors.

The Bernoulli numbers appear in the Taylor series expansions of the tangent and hyperbolic tangent functions, in formulas for the sum of powers of the first positive integers, in the Euler – Maclaurin formula, and in expressions for certain values of the Riemann zeta function.

For the first half of the decade, Maxis continued to produce expansions and sequels to The Sims, though EA's branding became more and more visible.

Plane Stupid then was launched in 2005, in an attempt to combat the growing airport expansions in the UK using direct action with a year later the first Camp for Climate Action being held with 600 people attending a protest called Reclaim Power converging on Drax Power Station in North Yorkshire and attempted to shut it down.

The first and second of four phases of development w ( which included the construction of a new enclosure for Greater Flamingos and Grey Crowned Cranes, as well as expansions for the giraffe enclosures, and a new cheetah encounter ) were completed in 2010

In April 1970, ground was broken for the first of many expansions.

, the original set and its expansions have been retired and replaced by a Party Box with the combined contents of the basic set and its first two expansions, and Party Box Expansion 1 set with the combined contents of the third and fourth expansions, and a Party Box Expansion 2, which contains new cards.

His Ph. D. thesis was advised by Yakov Borisovich Zel ' dovich and presented a first general-relativistic derivation of the conservative and radiation reaction forces in the Post-Newtonian expansions of the gravitational field of a binary system of two extended, massive bodies.

The size and population of the town remained fairly steady until the 1970s, at which point housebuilding began in earnest around the periphery of the town, first to the south ( 1950s – 70s ), then a series of major expansions to the west ( 1980s-present ) along the line of the railway.

At first, the game designers sought to introduce an entire new game based on Star Trek ; it would be simpler and be targeted to beginners, while the original game still produced expansions, but on a slower schedule.

This was the first of what were to be three major expansions, each centering around one of the principal characters.

Over the next few years, three expansions for the Pocket Box Illuminati game were published — the first two were substantially incorporated into the deluxe edition, while the third was an earlier version of what would become Illuminati: Brainwash.

While board game expansions are typically designed by the original creator, video game developers sometimes contract out development of the expansion pack to a third-party company, ( see Hellfire for Diablo ), it may choose to develop the expansion itself or it may do both ( Ensemble Studios developed the real-time strategy game Age of Empires III and the first expansion called the WarChiefs itself, but contracted Big Huge Games for the second expansion pack, the Asian Dynasties ).

The building underwent a series of expansions, first in 1916, then 1926 and finally in 1950, at the time giving the hotel a total of 1, 200 rooms.

; opens first store in Santo Domingo, capital city, with expansions to follow in all major cities of the country.

In March 2000, Verant released EverQuest: The Ruins of Kunark, the first in a long list of expansions for EverQuest.

The first of a number of expansions occurred in 1978, with the building that houses the Begley Library, a television station, lecture halls, and a wing for the music department along with the Carl B. Taylor Community Auditorium.

Extensions and expansions over the centuries led to its formal consecration in 1559 when the first bishop Nicolaas van Nieuwland was appointed.

Advised that to get a major league franchise Denver would need a much larger ballpark, Bears Stadium would begin the first of its many expansions.

In November 2006, Dawn of War and its first two expansions were released together as The Platinum Collection in the USA or as the Dawn of War Anthology in the PAL regions.