cp's OEIS Frontend

A328380 a(n) = (a(n-1) * a(n-3) - 2 * a(n-2)^2) / a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.

%I A328380 #29 Aug 15 2025 18:30:38
%S A328380 1,1,1,1,-1,-3,-5,-13,11,131,389,2311,9,-81511,-484247,-5751815,
%T A328380 -17124617,710017141,9644648819,204006839259,2405317965859,
%U A328380 -84560118880501,-2988387877551859,-105333970856330737,-3722531175803860975,130866937507290027313
%N A328380 a(n) = (a(n-1) * a(n-3) - 2 * a(n-2)^2) / a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
%C A328380 This is a (-1,2) generalized Somos-4 sequence.
%H A328380 Seiichi Manyama, <a href="/A328380/b328380.txt">Table of n, a(n) for n = 0..166</a>
%F A328380 a(n) = a(3-n) for all n in Z.
%F A328380 0 = a(n)*a(n+4) - a(n+1)*a(n+3) + 2*a(n+2)*a(n+2) for all n in Z.
%F A328380 0 = a(n)*a(n+5) - 2*a(n+1)*a(n+4) + a(n+2)*a(n+3) for all n in Z.
%F A328380 0 = a(n)*a(n+6) - 4*a(n+1)*a(n+5) - 7*a(n+3)*a(n+3) for all n in Z.
%F A328380 0 = a(n)*a(n+7) - a(n+1)*a(n+6) - 8*a(n+3)*a(n+4) for all n in Z.
%F A328380 A242107(2*n-3) = a(n) for all n in Z.
%t A328380 a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = (a[n - 1]*a[n - 3] - 2*a[n - 2]^2)/a[n - 4]; Array[a, 26, 0] (* _Amiram Eldar_, Jul 06 2020 *)
%t A328380 nxt[{a_,b_,c_,d_}]:={b,c,d,(d*b-2c^2)/a}; NestList[nxt,{1,1,1,1},30][[;;,1]] (* _Harvey P. Dale_, Aug 15 2025 *)
%o A328380 (PARI) {a(n) = my(v); if( n<0, n=3-n); n++; v = vector(max(4, n), k, 1); for(k=5, n, v[k] = (v[k-1] * v[k-3] - 2*v[k-2]^2) / v[k-4]); v[n]};
%o A328380 (PARI) {a(n) = my(m=2*n-3, E=ellinit([1, -1, 0, -1, 1]), z=ellpointtoz(E, [0, 1])); (-1)^n * round(ellsigma(E, m*z) / (ellsigma(E, z)^m^2 * 2^(n^2-3*n+2)))}; /* _Michael Somos_, Feb 25 2020 */
%Y A328380 Cf. A006720, A242107.
%K A328380 sign
%O A328380 0,6
%A A328380 _Michael Somos_, Feb 23 2020