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

Author

Simon Plouffe

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..830
• Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Programs

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 *)

PARI

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

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