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A178628 A (1,1) Somos-4 sequence associated to the elliptic curve E:y^2-xy-y=x^3+x^2+x. 0
1, 1, -1, -4, -3, 19, 67, -40, -1243, -4299, 25627, 334324, 627929, -29742841, -372632409, 1946165680, 128948361769, 1488182579081, -52394610324649, -2333568937567764, -5642424912729707, 3857844273728205019 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is (-1)^C(n,2) times the Hankel transform of the sequence with g.f.

1/(1-x^2/(1-x^2/(1-4x^2/(1+(3/16)x^2/(1-(76/9)x^2/(1-(201/361)x^2/(1-... where

1,4,-3/16,76/9,201/361,... are the x-coordinates of the multiples of z=(0,0)

on E:y^2-xy-y=x^3+x^2+x.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n)=(a(n-1)*a(n-3)+a(n-2)^2)/a(n-4), n>3.

PROG

(PARI) a(n)=local(E, z); E=ellinit([ -1, 1, -1, 1, 0]); z=ellpointtoz(E, [0, 0]); round(ellsigma(E, n*z)/ellsigma(E, z)^(n^2))

CROSSREFS

Sequence in context: A183231 A241358 A178417 * A167479 A220861 A076589

Adjacent sequences:  A178625 A178626 A178627 * A178629 A178630 A178631

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 31 2010

STATUS

approved

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Last modified December 20 07:03 EST 2014. Contains 252241 sequences.