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%I #11 Nov 05 2017 08:15:47
%S 1,2,3,5,9,16,28,50,93,178,342,650,1223,2302,4383,8480,16609,32658,
%T 63973,124375,240181,462597,893388,1737375,3407429,6729596,13336532,
%U 26415118,52129356,102359648,200067986,389989828,760206585,1485887074,2917775247,5759836217
%N Binomial transform of A010054 (characteristic function of triangular numbers).
%H Alois P. Heinz, <a href="/A143961/b143961.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) = Sum_{k=0..n} C(n,k) * A010054(k).
%e a(4) = [1,4,6,4,1]*[1,1,0,1,0] = 1+4+4 = 9.
%p 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 Table[Sum[Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%Y Cf. A000217, A007318, A010054.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Sep 05 2008
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