A171422 A (4,-5) Somos-4 sequence.

1, -1, -9, -41, -241, -271, 27329, 651521, 18425809, 399122991, -24055184809, -3943757411849, -498726356978849, -74609317288333151, 2771780972000481601, 8459493968101503667649, 5139175203350482789079649

Offset: 0

Author

Paul Barry, Dec 08 2009

Keywords

• easy
• sign

Comments

Hankel transform of A143013.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..109

Programs

Magma

I:=[1,-1,-9,-41]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) -5*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 18 2018

Mathematica

RecurrenceTable[{a[n] == (4*a[n-1]*a[n-3] -5*a[n-2]^2)/a[n-4], a[0] == 1, a[1] == -1, a[2] == -9, a[3] == -41}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *)

PARI

m=30; v=concat([1,-1,-9,-41], vector(m-4)); for(n=5, m, v[n] = ( 4*v[n-1]*v[n-3] -5*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 18 2018

Formula

a(n) = (4*a(n-1)*a(n-3) - 5*a(n-2)^2)/a(n-4), n>=3.