A163868 a(n) = (4^n + 11)/3.

4, 5, 9, 25, 89, 345, 1369, 5465, 21849, 87385, 349529, 1398105, 5592409, 22369625, 89478489, 357913945, 1431655769, 5726623065, 22906492249, 91625968985, 366503875929, 1466015503705, 5864062014809, 23456248059225, 93824992236889, 375299968947545

Offset: 0

Author

Juri-Stepan Gerasimov, Aug 08 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A002450, A047849, A156605.

Programs

Mathematica

LinearRecurrence[{5,-4}, {4,5}, 50] (* G. C. Greubel, Aug 06 2017 *)
(4^Range[0,30]+11)/3 (* Harvey P. Dale, Sep 10 2023 *)

PARI

x='x+O('x^50); Vec((4 - 15*x)/((4*x-1)*(x-1))) \\ G. C. Greubel, Aug 06 2017

Formula

a(n) = 4*a(n-1) - 11 = A155701(n) + 1 = A163834(n) + 2 = A047849(n) + 3.

From R. J. Mathar, Aug 11 2009: (Start)

a(n)= 5*a(n-1) - 4*a(n-2).

G.f.: (4 - 15*x)/((4*x-1)*(x-1)). (End)

E.g.f.: (1/3)*(exp(4*x) + 11*exp(x)). - G. C. Greubel, Aug 06 2017

Extensions

a(11) corrected by R. J. Mathar, Aug 11 2009