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

0,2

Links

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

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

Mathematica

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

Prog

(PARI) a(n) = if(n<2, max(0, n+1), 4*binomial(n-2, n\2-1))
(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
(SageMath) [4*binomial(n-2, ((n-2)//2)) + (n+1)*int(n<2) for n in range(41)] # G. C. Greubel, Oct 13 2022

Crossrefs

Cf. A047072, A063886.

Sequence in context: A245619 A131771 A335974 * A308528 A069753 A181245

Adjacent sequences: A047070 A047071 A047072 * A047074 A047075 A047076

Keyword

nonn

Author

Clark Kimberling

Status

approved