A188313 A (25,-29) Somos-4 sequence.

1, 3, 23, 314, 8209, 620297, 126742987, 47301104551, 32606721084786, 61958046554226593, 334806306946199122193, 3416372868727801226636179, 62595441409640805744780870839, 2993270782370572835241882188306602, 424202695773047673359251734568172738737

Offset: 0

Author

Paul Barry, Mar 28 2011

Keywords

• nonn
• easy

Comments

Hankel transform of A188312.

Examples

			G.f.: 1 + 3*x + 23*x^2 + 314*x^3 + 8209*x^4 + ... - _Michael Somos_, Feb 28 2022
		

Links

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

Crossrefs

Cf. A006720.

Programs

Magma

I:=[8209, 620297, 126742987, 47301104551]; [1, 3, 23, 314] 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, 3, 23, 314}, RecurrenceTable[{a[n] == (25*a[n - 1]*a[n - 3] - 29*a[n - 2]^2)/a[n - 4], a[4] == 8209, a[5] == 620297, a[6] == 126742987, a[7] == 47301104551}, a, {n, 4, 25}]]  (* G. C. Greubel, Aug 14 2018 *)
b[ n_] := If[OddQ[n], a[(n-3)/2], a[-n/2]]; a[ n_] := If[-2<=n<=2, {2, 1, 1, 3, 23}[[n+3]], 2*b[n+2]^3*b[n+3] + b[n+1]^2*(b[n+3]*b[n+4] - b[n+2]*b[n+5])]; (* Michael Somos, Feb 28 2022 *)

Formula

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

a(n) = b(-2*n) = b(2*n+3) = 2*b(n+2)^3*b(n+3) + b(n+1)^2*(b(n+3)*b(n+4) - b(n+2)*b(n+5)) for all n in Z where b(n) = A006720(n). - Michael Somos, Feb 28 2022