A174170 A (1,3) Somos-4 sequence.

1, -2, 1, 13, -23, -242, -1559, 16273, -145799, -4222034, 3164281, 3257872813, 94135157041, -7612225739042, 563989131103537, 69655619036668993, 4504341812743290961, -2245876068496447419362, -169454688152728033203119

Offset: 0

Author

Paul Barry, Mar 10 2010

Keywords

• easy
• sign

Comments

Hankel transform of A174169.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..122

Programs

Magma

I:=[1,-2,1,13]; [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 18 2018

Mathematica

RecurrenceTable[{a[n] == (a[n-1]*a[n-3] +3*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == -2, a[2] == 1, a[3] == 13}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *)

PARI

m=30; v=concat([1,-2,1,13], 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 18 2018

Formula

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

a(n) = a(-2-n) = (-3*a(n-1)*a(n-4) - 8*a(n-2)*a(n-3))/a(n-5) for all n in Z. - Michael Somos, May 04 2020