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

0,3

Comments

Diagonal sums of A100100.

Links

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A100100.

Sequence in context: A149344 A178078 A135489 * A149345 A149346 A149347

Adjacent sequences: A100214 A100215 A100216 * A100218 A100219 A100220

Keyword

easy,nonn

Author

Paul Barry, Nov 08 2004

Status

approved