A256916 a(n) = (a(n-1) * a(n-5) + a(n-3)^2) / a(n-6) with a(0) = a(1) = 1, a(2) = 0, a(3) = -1, a(4) = -3, a(8) = 29.

1, 1, 0, -1, -3, -3, -2, 9, 29, 83, 56, -243, -2351, -7227, -18648, 54011, 698301, 5324929, 15128062, -28437275, -1438167267, -14356619593, -108319050672, 80689859625, 13472837856577, 268773209122329, 2678522836045616, 7565687047045511, -672545703786704803

Offset: 0

Author

Michael Somos, Apr 13 2015

Keywords

• sign

Comments

Similar to the Somos-6 and Somos-7 sequences with many bilinear identities.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..208

Crossrefs

Cf. A102276, A256858.

Programs

Magma

I:=[83, 56, -243, -2351, -7227, -18648]; [1,1,0,-1,-3,-3,-2,9,29] cat [n le 6 select I[n] else (Self(n-1)*Self(n-5) + Self(n-3)^2)/ Self(n-6): n in [1..30]]; // G. C. Greubel, Aug 03 2018

Mathematica

Join[{1,1,0,-1,-3,-3,-2,9,29}, RecurrenceTable[{a[n] == (a[n-1]*a[n-5] + a[n-3]^2)/a[n-6], a[9] == 83, a[10] == 56, a[11] == -243, a[12] == -2351, a[13] == -7227, a[14] == -18648}, a, {n, 9, 60}]] (* G. C. Greubel, Aug 03 2018 *)

PARI

{a(n) = my(an); n = abs(n)+1; an = concat([ 1, 1, 0, -1, -3, -3, -2, 9, 29], vector(max(0, n-9), k)); for(k=10, n, an[k] = (an[k-1] * an[k-5] + an[k-3]^2) / an[k-6]); an[n]};

Formula

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

a(n) = A256858(2*n) for all n in Z.

Let b(n) = A102276(n). Then 0 = a(n) * b(n) - a(n+2) * b(n-2) + a(n+3) * b(n-3) for all n in Z.

0 = a(n) * a(n+6) - a(n+1) * a(n+5) - a(n+3) * a(n+3) for all n in Z.

0 = a(n) * a(n+9) + a(n+2) * a(n+7) - a(n+3) * a(n+6) - 9 * a(n+4) * a(n+5) for all n in Z.