A188315 A (25,-29) Somos-4 sequence.

1, 1, -4, -129, -3689, -113689, 7001471, 7911171596, 6480598259201, 5987117709349201, -4830209396684261199, -230318343950087449971199, -5423908604123397486016003604, -147547506573676549005535542233729, 739578212227710098047348234126634311

Offset: 0

Author

Paul Barry, Mar 28 2011

Keywords

• sign
• easy

Comments

Hankel transform of A188314.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..74

Programs

Magma

I:=[-3689, -113689, 7001471, 7911171596]; [1, 1, -4, -129] cat [n le 4 select I[n] else (25*Self(n-1)*Self(n-3) - 29*Self(n-2)^2 )/Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018

Mathematica

Join[{1, 1, -4, -129}, RecurrenceTable[{a[n] == (25*a[n - 1]*a[n - 3] - 29*a[n - 2]^2)/a[n - 4], a[4] == -3689, a[5] == -113689, a[6] == 7001471, a[7] == 7911171596}, a, {n, 4, 25}]]  (* G. C. Greubel, Aug 14 2018 *)
nxt[{a_,b_,c_,d_}]:={b,c,d,(25d*b-29c^2)/a}; NestList[nxt,{1,1,-4,-129},20][[All,1]] (* Harvey P. Dale, Aug 04 2022 *)

Formula

a(n) = (25*a(n-1)*a(n-3) - 29*a(n-2)^2)/a(n-4), n>=4.