A047073 a(n) = Sum_{j=0..n} A047072(j, n-j).

1, 2, 4, 4, 8, 12, 24, 40, 80, 140, 280, 504, 1008, 1848, 3696, 6864, 13728, 25740, 51480, 97240, 194480, 369512, 739024, 1410864, 2821728, 5408312, 10816624, 20801200, 41602400, 80233200, 160466400, 310235040, 620470080, 1202160780

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A047072, A063886.

Programs

Magma

[n le 1 select n+1 else 4*Binomial(n-2, Floor((n-2)/2)): n in [0..40]]; // G. C. Greubel, Oct 13 2022

Mathematica

Table[If[n<2, n+1, 4*Binomial[n-2, Floor[(n-2)/2]]], {n,0,40}] (* G. C. Greubel, Oct 13 2022 *)

PARI

a(n) = if(n<2, max(0,n+1), 4*binomial(n-2, n\2-1))

SageMath

[4*binomial(n-2, ((n-2)//2)) + (n+1)*int(n<2) for n in range(41)] # G. C. Greubel, Oct 13 2022

Formula

a(n) = 2*A063886(n-1) + (n+1)*[n<2].

G.f.: 1 + 2*x*sqrt((1+2*x)/(1-2*x)). - Michael Somos

E.g.f.: 1 - x*BesselI(1, 2*x)*(2 + Pi*(1 + 2*x)*StruveL(0, 2*x)) + x*(1 + 2*x)*BesselI(0, 2*x)*(2 + Pi*StruveL(1, 2*x)). - Stefano Spezia, May 11 2024