A184121 A (4,-3) Somos-4 sequence.

1, -1, -7, -31, -23, 2239, 39889, 603521, -27466831, -2445382081, -204734091383, 7545563759329, 7265319037194073, 2502938339020429439, 404477135616551491361, -932929530161758614571519

Offset: 0

Author

Paul Barry, Jan 09 2011

Keywords

• sign
• easy

Comments

Hankel transform of A184120.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..75

Programs

Magma

I:=[-23, 2239, 39889, 603521]; [1, -1, -7, -31] cat [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) - 3*Self(n-2)^2 )/Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018

Mathematica

RecurrenceTable[{a[0]==1,a[1]==-1,a[2]==-7,a[3]==-31,a[n]==(4a[n-1] a[n-3]- 3a[n-2]^2)/a[n-4]},a,{n,20}] (* Harvey P. Dale, Apr 03 2016 *)

Formula

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