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%I #12 Sep 08 2022 08:45:41
%S 1,-1,-5,-4,29,129,-65,-3689,-16264,113689,2382785,7001471,-398035821,
%T -7911171596,43244638645,6480598259201,124106986093951,
%U -5987117709349201,-541051130050800400,-4830209396684261199
%N A Somos-4 variant.
%C Hankel transform of A157100.
%H G. C. Greubel, <a href="/A157101/b157101.txt">Table of n, a(n) for n = 0..145</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) + a(n-2)^2)/a(n-4), with a(0)=1, a(1)=-1, a(2)=-5, a(3)=-4.
%F a(n) = A051138(n+1) for all n in Z. - _Michael Somos_, Jul 17 2016
%t RecurrenceTable[{a[n]==(a[n-1]*a[n-3]+a[n-2]^2)/a[n-4], a[0]==1, a[1]==-1, a[2]==-5, a[3]==-4}, a, {n,20}] (* _G. C. Greubel_, Feb 23 2019 *)
%o (PARI) m=20; v=concat([1,-1,-5,-4], vector(m-4)); for(n=5, m, v[n] = (v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Feb 23 2019
%o (Magma) I:=[1,-1,-5,-4]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..20]]; // _G. C. Greubel_, Feb 23 2019
%o (Sage)
%o def a(n):
%o if (n==0): return 1
%o elif (n==1): return -1
%o elif (n==2): return -5
%o elif (n==3): return -4
%o else: return (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
%o [a(n) for n in (0..20)] # _G. C. Greubel_, Feb 23 2019
%o (GAP) a:=[1,-1,-5,-4];; for n in [5..20] do a[n]:=(a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # _G. C. Greubel_, Feb 23 2019
%Y Cf. A051138.
%Y Cf. A157005, A162546, A162547.
%K easy,sign
%O 0,3
%A _Paul Barry_, Feb 22 2009
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