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%I #10 Sep 08 2022 08:45:53
%S 1,1,-2,-3,-5,-28,67,411,-506,10855,-74231,-664776,7518457,-30009367,
%T 1791756790,22973709333,-762305126477,-10339529833556,
%U -516074985082229,-26431010871217485,1057255130388472846
%N A (-1,-2) Somos-4 sequence associated to the elliptic curve y^2 +y = x^3 +3*x^2 +x.
%C Hankel transform of the sequence with g.f. 1/(1-x^2/(1+2x^2/(1+(3/4)x^2/(1-(10/9)x^2/(1-...,
%C where -2,-3/4,10/9,... are the x-coordinates of the multiples of (0,0).
%H G. C. Greubel, <a href="/A178376/b178376.txt">Table of n, a(n) for n = 0..154</a>
%H Paul Barry, <a href="https://arxiv.org/abs/1910.00875">Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials</a>, arXiv:1910.00875 [math.CO], 2019.
%F a(n) = (-a(n-1)*a(n-3) - 2*a(n-2)^2)/a(n-4), n>3.
%t RecurrenceTable[{a[n]==(-a[n-1]*a[n-3] -2*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == -2, a[3] == -3}, a, {n, 0, 30}] (* _G. C. Greubel_, Sep 16 2018 *)
%o (PARI) m=30; v=concat([1,1,-2,-3], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] - 2*v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Sep 16 2018
%o (Magma) I:=[1,1,-2,-3]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) - 2*Self(n-2)^2)/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Sep 16 2018
%K easy,sign
%O 0,3
%A _Paul Barry_, May 26 2010
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