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A178627
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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, -2, -1, 5, 9, -8, -41, -61, 241, 770, -271, -8649, -27329, 106768, 651521, 740665, -18425809, -107300098, 399122991, 5615422669, 24055184809, -383354254360, -3943757411849, 9276714153611, 498726356978849
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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/(1-2x^2/(1-(1/4)x^2/(1-10x^2/(1-(9/25)x^2/(1-... where
1,2,-1/4,10,9/25,... 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..26.
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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: A193629 A021467 A011132 * A019098 A035309 A174218
Adjacent sequences: A178624 A178625 A178626 * A178628 A178629 A178630
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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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