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A143961 Binomial transform of A010054 (characteristic function of triangular numbers). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 13:34 EST 2019. Contains 319271 sequences. (Running on oeis4.)