A178377 A (-1,-3) Somos-4 sequence associated to y^2 + y = x^3 + 4*x^2 + x.

1, 1, -3, -5, -22, -141, 719, 8765, 14319, 1707596, -21672017, -962616165, 16392942967, -1419903481091, 100267906812546, 7990790144939605, -1147738310571578779, 53860607055523082151, -43705893899966302362943

Offset

0,3

Comments

Hankel transform of the sequence with g.f. 1/(1-x/(1+3x^2/(1+(5/9)x^2/91-(66/25)x^2/(1-...,

where -3,-5/9,66/25,... are the x-coordinates of the multiples of (0,0).

Links

G. C. Greubel, Table of n, a(n) for n = 0..124

Formula

a(n) = (-a(n-1)*a(n-3) - 3*a(n-2)^2)/a(n-4), n>3.

Mathematica

RecurrenceTable[{a[n]==(-a[n-1]*a[n-3] -3*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 1, a[2] == -3, a[3] == -5}, a, {n, 0, 30}] (* G. C. Greubel, Sep 16 2018 *)

Prog

(PARI) m=30; v=concat([1, 1, -3, -5], vector(m-4)); for(n=5, m, v[n] = ( -v[n-1]*v[n-3] - 3*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 16 2018
(Magma) I:=[1, 1, -3, -5]; [n le 4 select I[n] else (-Self(n-1)*Self(n-3) - 3*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 16 2018

Crossrefs

Sequence in context: A124423 A209109 A212260 * A270621 A270637 A064187

Adjacent sequences: A178374 A178375 A178376 * A178378 A178379 A178380

Keyword

easy,sign

Author

Paul Barry, May 26 2010

Status

approved