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Search: id:A097496
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| A097496 |
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Subsequence of terms of odd index of the Somos-5 sequence. |
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1
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| 1, 1, 2, 5, 37, 274, 6161, 165713, 9434290, 1013908933, 142844426789, 57760865728994, 23510036246274433, 29636604976524724225, 42939094881045167060258, 139127528853472250968193381
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OFFSET
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0,3
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COMMENT
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The sequence corresponds to the sequence of points Q+nP on the curve y^2=4*x^3-(121/12)*x+845/216, where Q=(-7/12,-3) and P=(17/12,-1).
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REFERENCES
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A. N. W. Hone, Elliptic curves and quadratic recurrence sequences, Bull. Lond. Math. Soc. 37 (2005) 161-171.
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FORMULA
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a(0)=a(1)=1, a(2)=2, a(3)=5; a(n) = (a(n-1)*a(n-3)+8*a(n-2)^2)/a(n-4).
Exact formula: a(n)=D*E^n*sigma(f+n*k)/sigma(k)^(n^2) where sigma is the Weierstrass sigma function associated to the elliptic curve y^2=4*x^3-(121/12)*x+845/216, D=1/sigma(f)=-0.363554228-0.803200610*I, E=sigma(k)*sigma(f)/sigma(f+k)=0.644801269+0.734118205*I, f=\int_{\infty}^{-7/12} dx/y = -0.509286773+0.973928783*I, k=\int_{17/12}^{\infty} dx/y = 1.018573545 all to 9 d.p.
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MAPLE
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a[0]:=1; a[1]:=1; a[2]:=2; a[3]:=5; for n from 1 to 20 do a[n+3]:=(a[n+2]*a[n]+8*a[n+1]^2)/a[n-1] od;
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CROSSREFS
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Cf. A006721, A006720.
Sequence in context: A138658 A067464 A081545 this_sequence A099657 A107633 A041959
Adjacent sequences: A097493 A097494 A097495 this_sequence A097497 A097498 A097499
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KEYWORD
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nonn
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AUTHOR
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Andrew Hone (anwh(AT)kent.ac.uk), Aug 24 2004
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