A143961 Binomial transform of A010054 (characteristic function of triangular numbers).

1, 2, 3, 5, 9, 16, 28, 50, 93, 178, 342, 650, 1223, 2302, 4383, 8480, 16609, 32658, 63973, 124375, 240181, 462597, 893388, 1737375, 3407429, 6729596, 13336532, 26415118, 52129356, 102359648, 200067986, 389989828, 760206585, 1485887074, 2917775247, 5759836217

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{k=0..n} C(n,k) * A010054(k).

Example

a(4) = [1,4,6,4,1]*[1,1,0,1,0] = 1+4+4 = 9.

Maple

a:= proc(n) local k, i, s; k:=0; i:=0; s:=0; while k<=n do s:= s+binomial(n, k); i:=i+1; k:=k+i; od; s end: seq(a(n), n=0..40);

Mathematica

Table[Sum[Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 30 2017 *)

Crossrefs

Cf. A000217, A007318, A010054.

Sequence in context: A088352 A002572 A114834 * A128023 A000048 A056303

Adjacent sequences: A143958 A143959 A143960 * A143962 A143963 A143964

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2008

Status

approved