# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a143961 Showing 1-1 of 1 %I A143961 #11 Nov 05 2017 08:15:47 %S A143961 1,2,3,5,9,16,28,50,93,178,342,650,1223,2302,4383,8480,16609,32658, %T A143961 63973,124375,240181,462597,893388,1737375,3407429,6729596,13336532, %U A143961 26415118,52129356,102359648,200067986,389989828,760206585,1485887074,2917775247,5759836217 %N A143961 Binomial transform of A010054 (characteristic function of triangular numbers). %H A143961 Alois P. Heinz, Table of n, a(n) for n = 0..1000 %H A143961 N. J. A. Sloane, Transforms %F A143961 a(n) = Sum_{k=0..n} C(n,k) * A010054(k). %e A143961 a(4) = [1,4,6,4,1]*[1,1,0,1,0] = 1+4+4 = 9. %p A143961 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); %t A143961 Table[Sum[Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* _Vaclav Kotesovec_, Oct 30 2017 *) %Y A143961 Cf. A000217, A007318, A010054. %K A143961 nonn %O A143961 0,2 %A A143961 _Alois P. Heinz_, Sep 05 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE