

A178628


A (1,1) Somos4 sequence associated to the elliptic curve E:y^2xyy=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
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OFFSET

0,4


COMMENTS

a(n) is (1)^C(n,2) times the Hankel transform of the sequence with g.f.
1/(1x^2/(1x^2/(14x^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 xcoordinates of the multiples of z=(0,0)
on E:y^2xyy=x^3+x^2+x.


LINKS

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


FORMULA

a(n)=(a(n1)*a(n3)+a(n2)^2)/a(n4), 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



