A084643 a(n) = 3^(n-1)*(2*n-3) + 2^(n+1).

1, 3, 11, 43, 167, 631, 2315, 8275, 28943, 99439, 336659, 1126027, 3728279, 12239527, 39890843, 129205699, 416249375, 1334710495, 4262149667, 13560765691, 43005771431, 135988785943, 428882869931, 1349402340403

Offset: 0

Author

Paul Barry, Jun 09 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A048495. Second binomial transform of 1, 1, 3, 5, 7, ...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-21,18).

Crossrefs

Cf. A048495, A060747.

Programs

Magma

[3^(n-1)*(2*n-3)+2^(n+1) : n in [0..30]]; // Vincenzo Librandi, Sep 25 2011

Mathematica

LinearRecurrence[{8,-21,18},{1,3,11},30] (* Harvey P. Dale, Dec 12 2015 *)

PARI

Vec((1-5*x+8*x^2)/(1-2*x)/(1-3*x)^2+O(x^99)) \\ Charles R Greathouse IV, Mar 22 2012

SageMath

[2^(n+1) +3^(n-1)*(2*n-3) for n in range(41)] # G. C. Greubel, Mar 22 2023

Formula

G.f.: (1 - 5*x + 8*x^2)/((1-2*x)*(1-3*x)^2). - Colin Barker, Mar 22 2012

E.g.f.: 2*exp(2*x) + (2*x-1)*exp(3*x). - G. C. Greubel, Mar 22 2023