A174017 A (1,1) Somos-4 sequence.

1, 2, -3, 1, 11, -16, -35, -129, 299, -386, -3977, 8063, 42489, 269344, -1000009, 3727745, 47166649, -123526014, -1764203419, -18228952703, 113727892147, -1065812586544, -18344075481339, 52130069331199, 2470319425874195

Offset: 0

Author

Paul Barry, Mar 05 2010

Keywords

• easy
• sign

Comments

Hankel transform of A174013.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..150

Programs

Magma

I:=[1,2,-3,1]; [n le 4 select I[n] else (Self(n-1)*Self(n-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] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == -3, a[3] == 1}, a, {n, 0, 150}] (* G. C. Greubel, Sep 18 2018 *)
nxt[{a_,b_,c_,d_}]:={b,c,d,(b*d+c^2)/a}; NestList[nxt,{1,2,-3,1},30][[All,1]] (* Harvey P. Dale, Jun 21 2022 *)

PARI

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

Formula

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