A174634 - OEIS

A174634

a(n) = 3^n * Fibonacci(n+2).

1, 6, 27, 135, 648, 3159, 15309, 74358, 360855, 1751787, 8503056, 41275251, 200353257, 972537030, 4720790403, 22915204479, 111232727064, 539935021503, 2620899608085, 12722114017782, 61754438526111, 299762341738371, 1455076971950112, 7063091991495675, 34284968722038033

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,9).

FORMULA

G.f.: (1+3*x)/(1-3*x-9*x^2) = 1/(-3*x-1/(-3*x-1)).

a(n) = (1/2+3*sqrt(5)/10)*(3/2+3*sqrt(5)/2)^n + (1/2-3*sqrt(5)/10)*(3/2-3*sqrt(5)/2)^n.

E.g.f.: exp(3*x/2) * (cosh(sqrt(5)*3*x/2) + 3*sinh(sqrt(5)*3*x/2)/sqrt(5)). - Amiram Eldar, Feb 06 2026

MATHEMATICA

Table[3^n Fibonacci[n+2], {n, 0, 30}] (* or *) LinearRecurrence[{3, 9}, {1, 6}, 30] (* Harvey P. Dale, May 23 2014 *)