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A178628
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A (1,1) Somos-4 sequence associated to the elliptic curve E:y^2-xy-y=x^3+x^2+x.
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0
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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
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0,4
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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a(n)=(a(n-1)*a(n-3)+a(n-2)^2)/a(n-4), n>3.
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PROG
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(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))
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CROSSREFS
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Sequence in context: A192773 A183231 A178417 * A167479 A220861 A076589
Adjacent sequences: A178625 A178626 A178627 * A178629 A178630 A178631
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, May 31 2010
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STATUS
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approved
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