A026624 a(n) = Sum_{j=0..n} Sum_{k=0..j} A026615(j, k).

1, 3, 8, 20, 46, 100, 210, 432, 878, 1772, 3562, 7144, 14310, 28644, 57314, 114656, 229342, 458716, 917466, 1834968, 3669974, 7339988, 14680018, 29360080, 58720206, 117440460, 234880970, 469761992, 939524038, 1879048132

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.

Cf. A026622, A026623, A026625, A026956, A026957, A026958, A026959.

Cf. A026960.

Programs

Magma

[1] cat [n le 1 select 3 else 2*Self(n-1) + 2*(n-1): n in [1..41]]; // G. C. Greubel, Jun 15 2024

Mathematica

Table[(7*2^n -4*(n+1) -Boole[n==0])/2, {n,0,40}] (* G. C. Greubel, Jun 15 2024 *)

SageMath

[(7*2^n -4*(n+1) -int(n==0))/2 for n in range(41)] # G. C. Greubel, Jun 15 2024

Formula

G.f.: (1-x+x^2+x^3)/((1-x)^2*(1-2*x)) (Cf. A026622). - Ralf Stephan, Feb 05 2004

From G. C. Greubel, Jun 15 2024: (Start)

a(n) = 2*a(n-1) + 2*(n-1), with a(0) = 1, a(1) = 3.

a(n) = 7*2^(n-1) - 2*(n+1) - (1/2)*[n=0].

E.g.f.: (1/2)*( 7*exp(2*x) - 4*(x+1)*exp(x) - 1). (End)