A020532 a(n) = 6th Fibonacci polynomial evaluated at 2^n.

8, 70, 1292, 34840, 1065008, 33685600, 1074790592, 34368127360, 1099578737408, 35184908961280, 1125904201812992, 36028831378708480, 1152921779484766208, 36893490346442383360, 1180591638309597396992, 37778932003694650163200, 1208925820740529081745408

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..664

Index entries for linear recurrences with constant coefficients, signature (42,-336,512).

Formula

From Colin Barker, May 03 2015: (Start)

a(n) = 2^n*(3+4^(1+n)+16^n).

a(n) = 42*a(n-1)-336*a(n-2)+512*a(n-3) for n>2.

G.f.: -2*(520*x^2-133*x+4) / ((2*x-1)*(8*x-1)*(32*x-1)).

(End)

Maple

with(combinat, fibonacci):seq(fibonacci(6, 2^i), i=0..24);

Mathematica

Table[Fibonacci[6, 2^i], {i, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
LinearRecurrence[{42, -336, 512}, {8, 70, 1292}, 20] (* Harvey P. Dale, Aug 04 2023 *)

Prog

(PARI) Vec(-2*(520*x^2-133*x+4)/((2*x-1)*(8*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015

Crossrefs

Sequence in context: A266433 A267244 A228388 * A043086 A003364 A376053

Adjacent sequences: A020529 A020530 A020531 * A020533 A020534 A020535

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved