A020531 a(n) = 5th Fibonacci polynomial evaluated at 2^n.

5, 29, 305, 4289, 66305, 1051649, 16789505, 268484609, 4295163905, 68720263169, 1099514773505, 17592198627329, 281475027042305, 4503599828697089, 72057594843234305, 1152921507828072449, 18446744086594453505, 295147905230892433409, 4722366483075803643905

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..830

Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Formula

From Colin Barker, May 03 2015: (Start)

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

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n > 2.

G.f.: -(116*x^2 - 76*x + 5)/((x - 1)*(4*x - 1)*(16*x - 1)). (End)

E.g.f.: exp(x)*(1 + 3*exp(3*x) + exp(15*x)). - Stefano Spezia, Jul 31 2022

Maple

with(combinat, fibonacci):seq(fibonacci(5, 2^i), i=0..24);

Mathematica

Table[Fibonacci[5, 2^i], {i, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)

Prog

(PARI) Vec(-(116*x^2-76*x+5)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015

Crossrefs

Sequence in context: A332517 A332469 A112799 * A195228 A226668 A226666

Adjacent sequences: A020528 A020529 A020530 * A020532 A020533 A020534

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved