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.

1, 1, 1, 1, -1, -3, -5, -13, 11, 131, 389, 2311, 9, -81511, -484247, -5751815, -17124617, 710017141, 9644648819, 204006839259, 2405317965859, -84560118880501, -2988387877551859, -105333970856330737, -3722531175803860975, 130866937507290027313

Offset

0,6

Comments

This is a (-1,2) generalized Somos-4 sequence.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..166

Formula

a(n) = a(3-n) for all n in Z.

0 = a(n)*a(n+4) - a(n+1)*a(n+3) + 2*a(n+2)*a(n+2) for all n in Z.

0 = a(n)*a(n+5) - 2*a(n+1)*a(n+4) + a(n+2)*a(n+3) for all n in Z.

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.

0 = a(n)*a(n+7) - a(n+1)*a(n+6) - 8*a(n+3)*a(n+4) for all n in Z.

A242107(2*n-3) = a(n) for all n in Z.

Mathematica

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 *)

Prog

(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]};
(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 */

Crossrefs

Cf. A006720, A242107.

Sequence in context: A171424 A231897 A260416 * A256222 A258976 A348659

Adjacent sequences: A328377 A328378 A328379 * A328381 A328382 A328383

Keyword

sign

Author

Michael Somos, Feb 23 2020

Status

approved