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A143961
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Binomial transform of A010054 (characteristic function of triangular numbers).
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} C(n,k) * A010054(k).
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EXAMPLE
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a(4) = [1,4,6,4,1]*[1,1,0,1,0] = 1+4+4 = 9.
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MAPLE
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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);
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MATHEMATICA
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Table[Sum[Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 30 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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