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%I #19 Sep 08 2022 08:46:07
%S -1,0,1,12,-432,93312,241864704,-940369969152,-29249267520503808,
%T -6823269127183128330240,5348220265883981394311380992,
%U 2566558951457996941025058427502592,-336245011425341849227546073789919098044416
%N a(0)-a(5) are -1, 0, 1, 12, -432, 93312; thereafter a(n) = (144*a(n-3)*a(n-1)+432*a(n-2)^2)/a(n-4).
%H G. C. Greubel, <a href="/A241593/b241593.txt">Table of n, a(n) for n = 0..54</a>
%H R. W. Gosper and Richard C. Schroeppel, <a href="https://arxiv.org/abs/math/0703470">Somos Sequence Near-Addition Formulas and Modular Theta Functions</a>, arXiv:math/0703470 [math.NT], 2007. See p. 18.
%p f:=proc(n) option remember;
%p if n <= 2 then n-1
%p elif n=3 then 12
%p elif n=4 then -432
%p elif n=5 then 93312
%p else (144*f(n-3)*f(n-1)+432*f(n-2)^2)/f(n-4); fi; end;
%p (144*a(n-3)*a(n-1)+432*a(n-2)^2)/a(n-4); ai; end;
%p [seq(f(n),n=0..15)];
%t a[n_] := a[n] = Which[n <= 2, n - 1, n == 3, 12, n == 4, -432, n == 5, 93312, True, (144*a[n - 3]*a[n - 1] + 432 a[n - 2]^2)/a[n - 4]];
%t Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Dec 05 2017 *)
%t nxt[{a_,b_,c_,d_}]:={b,c,d,(144b*d+432c^2)/a}; Join[{-1,0},NestList[nxt,{1,12,-432,93312},10][[All,1]]] (* _Harvey P. Dale_, Dec 30 2017 *)
%o (Magma) I:=[1,12,-432,93312]; [-1, 0] cat [n le 4 select I[n] else (144*Self(n-3)*Self(n-1) + 432*Self(n - 2)^2)/Self(n-4): n in [1..20]]; // _G. C. Greubel_, Aug 08 2018
%K sign
%O 0,4
%A _N. J. A. Sloane_, May 16 2014
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