A163834 a(n) = (4^n + 5)/3.

2, 3, 7, 23, 87, 343, 1367, 5463, 21847, 87383, 349527, 1398103, 5592407, 22369623, 89478487, 357913943, 1431655767, 5726623063, 22906492247, 91625968983, 366503875927, 1466015503703, 5864062014807, 23456248059223, 93824992236887, 375299968947543

Offset: 0

Author

Juri-Stepan Gerasimov, Aug 05 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. A000027, A135351, A140966, A153643.

Programs

Mathematica

Table[(4^n + 5)/3, {n, 0, 50}] (* G. C. Greubel, Aug 05 2017 *)
LinearRecurrence[{5,-4},{2,3},30] (* Harvey P. Dale, Jun 14 2023 *)

PARI

x='x+O('x^50); concat([0], Vec((2-7*x)/((4*x-1)*(x-1)))) \\ G. C. Greubel, Aug 05 2017

Formula

a(n) = (4^n + 5)/3 = A135351(2*n+1) = A140966(2*n) = A153643(2*n).

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

G.f.: (2-7*x)/((4*x-1)*(x-1)).

a(n+1) - a(n) = A000302(n).

E.g.f.: (1/3)*(5*exp(x) + exp(4*x)). - G. C. Greubel, Aug 05 2017

Extensions

Offset set to 0 by R. J. Mathar, Aug 06 2009