A143962 Binomial transform of A066247 (characteristic function of composite numbers).
0, 0, 0, 0, 1, 5, 16, 42, 99, 220, 476, 1023, 2201, 4732, 10102, 21284, 44103, 89845, 180354, 358226, 707561, 1396560, 2764906, 5501807, 11005363, 22101301, 44470622, 89475559, 179753753, 360325116, 720748862, 1439561539, 2873846383, 5740501232, 11484167472
Offset: 0
Keywords
Examples
a(7) = [35,21,7,1]*[1,0,1,0] = 35+7 = 42.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- N. J. A. Sloane, Transforms
Programs
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Maple
a:= proc(n) local k,s; s:=0; for k from 4 to n do if not isprime(k) then s:= s+ binomial(n,k) fi od; s; end: seq (a(n), n=0..40);
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Mathematica
a[n_] := Module[{k, s = 0}, For[k = 4, k <= n, k++, If[!PrimeQ[k], s = s + Binomial[n, k]]]; s]; Table [a[n], {n, 0, 40}] // Flatten (* Jean-François Alcover, Dec 30 2013, translated from Maple *)
Formula
a(n) = Sum_{k=4..n} C(n,k)*A066247(k).