A049675 a(n) = (2*F(3*n) - F(n))/3, where F=A000045 (the Fibonacci sequence).

0, 1, 5, 22, 95, 405, 1720, 7293, 30905, 130934, 554675, 2349689, 9953520, 42163913, 178609405, 756601910, 3205017655, 13576673517, 57511713320, 243623529381, 1032005835025, 4371646876246, 18518593350955

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-2,-5,-1).

Formula

G.f.: -x*(x-1)*(1+x) / ( (x^2+4*x-1)*(x^2+x-1) ). - R. J. Mathar, Nov 10 2013

a(n) = F(n) + 2*Sum_{k=1..n} F(n-k)*F(3*k), where F=A000045 (the Fibonacci sequence). - Yomna Bakr and Greg Dresden, Jun 17 2024

Mathematica

Table[(2Fibonacci[3n]-Fibonacci[n])/3, {n, 0, 30}] (* Harvey P. Dale, Dec 08 2012 *)
LinearRecurrence[{5, -2, -5, -1}, {0, 1, 5, 22}, 30] (* G. C. Greubel, Dec 02 2017 *)

Prog

(PARI) for(n=0, 30, print1((2*fibonacci(3*n) - fibonacci(n))/3, ", ")) \\ G. C. Greubel, Dec 02 2017
(Magma) [(2*Fibonacci(3*n) - Fibonacci(n))/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Crossrefs

Sequence in context: A049652 A026877 A128746 * A053154 A141222 A127360

Adjacent sequences: A049672 A049673 A049674 * A049676 A049677 A049678

Keyword

nonn

Author

Clark Kimberling

Status

approved