A100217 Diagonal sums of a binomial number triangle.

1, 1, 4, 12, 42, 149, 543, 2007, 7501, 28265, 107196, 408653, 1564506, 6010964, 23164467, 89501021, 346588092, 1344804060, 5227147969, 20349230347, 79330194097, 309653982738, 1210071825851, 4733665388134, 18535196846866

Offset: 0

Author

Paul Barry, Nov 08 2004

Keywords

• easy
• nonn

Comments

Diagonal sums of A100100.

Links

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

Crossrefs

Cf. A100100.

Programs

Magma

[(&+[Binomial(2*n-3*k-1, n-2*k): k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Mar 28 2024

Mathematica

A100217[n_]:= Sum[Binomial[2*n-3*k-1,n-2*k], {k,0,Floor[n/2]}];
Table[A100217[n], {n,0,40}] (* G. C. Greubel, Mar 28 2024 *)

SageMath

[sum(binomial(2*n-3*k-1, n-2*k) for k in range(1+n//2)) for n in range(41)] # G. C. Greubel, Mar 28 2024

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1, n-2*k).