A086972 a(n) = n*3^(n-1) + (3^n + 1)/2.

1, 3, 11, 41, 149, 527, 1823, 6197, 20777, 68891, 226355, 738113, 2391485, 7705895, 24712007, 78918989, 251105873, 796364339, 2518233179, 7942120025, 24988621541, 78452649023, 245818300271, 768835960421, 2400651060089

Offset: 0

Author

Paul Barry, Jul 26 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A057711 (without leading zero). Second binomial transform of (1,1,3,3,5,5,7,7,9,9,11,11,...).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (7,-15,9).

Crossrefs

Cf. A007051, A027471, A057711, A081038.

Partial sums of A199923.

Programs

Magma

[n*3^(n-1) + (3^n+1)/2: n in [0..30]]; // Vincenzo Librandi, Jun 09 2011

Mathematica

Table[((2*n+3)*3^(n-1) +1)/2, {n,0,30}] (* G. C. Greubel, Nov 24 2023 *)

PARI

Vec((1-4*x+5*x^2)/((1-x)*(1-3*x)^2) + O(x^40)) \\ Michel Marcus, Mar 08 2016

SageMath

[((2*n+3)*3^(n-1) +1)//2 for n in range(31)] # G. C. Greubel, Nov 24 2023

Formula

a(n) = (1/2)*(A081038(n) + 1).

G.f.: (1-4*x+5*x^2)/((1-x)*(1-3*x)^2).

a(n) = A027471(n) + A007051(n).

E.g.f.: (1/2)*( exp(x) + (2*x+1)*exp(3*x) ). - G. C. Greubel, Nov 24 2023