A212262 a(n) = 3^n + Fibonacci(n).

1, 4, 10, 29, 84, 248, 737, 2200, 6582, 19717, 59104, 177236, 531585, 1594556, 4783346, 14349517, 43047708, 129141760, 387423073, 1162265648, 3486791166, 10460364149, 31381077320, 94143207484, 282429582849, 847288684468, 2541865949722, 7625597681405, 22876792772772

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).

Formula

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

E.g.f.: cosh(3*x) + sinh(3*x) + 2*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Oct 26 2025

Mathematica

Table[3^n + Fibonacci[n], {n, 0, 27}]

Prog

(PARI) for(n=0, 27, print1(3^n+fibonacci(n)", "));
(Magma) [3^n+Fibonacci(n): n in [0..27]];
(SageMath) [3^n +fibonacci(n) for n in (0..30)] # G. C. Greubel, Jul 05 2021

Crossrefs

Cf. A000045, A000244, A001611, A117591, A212323.

Sequence in context: A025179 A116388 A221420 * A233347 A264158 A390111

Adjacent sequences: A212259 A212260 A212261 * A212263 A212264 A212265

Keyword

nonn,easy

Author

Bruno Berselli, May 08 2012

Status

approved