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A052284
Number of compositions of n into nonprime numbers.
24
1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27, 40, 61, 92, 142, 217, 333, 506, 774, 1181, 1807, 2758, 4215, 6434, 9833, 15019, 22948, 35047, 53541, 81780, 124936, 190841, 291532, 445320, 680274, 1039155, 1587405, 2424849, 3704148, 5658321, 8643530
OFFSET
0,5
COMMENTS
Starting at n=1, appears to be row sums of triangle A157424. - Gary W. Adamson & Mats Granvik, Feb 28 2009
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5437 (first 501 terms from T. D. Noe)
FORMULA
G.f.: 1/( 1 - (Sum_{m nonprime} x^m) ).
EXAMPLE
a(6) = 5 because 1+1+1+1+1+1 = 1+1+4 = 1+4+1 = 4+1+1 = 6.
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(isprime(j), 0, a(n-j)), j=1..n))
end:
seq(a(n), n=0..45); # Alois P. Heinz, Aug 06 2019
MATHEMATICA
nn=50; np=Select[Range[nn], !PrimeQ[ # ] &]; CoefficientList[Series[1/(1-Sum[x^k, {k, np}]), {x, 0, nn}], x] (* T. D. Noe, Aug 20 2010 *)
CROSSREFS
Cf. A002095 (Number of partitions of n into nonprime parts).
Column k=0 of A224344.
Sequence in context: A072465 A204631 A323361 * A133670 A356627 A127272
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, May 16 2002
EXTENSIONS
Definition and g.f. corrected by N. J. A. Sloane, Aug 19 2010, who thanks Vladimir Kruchinin for pointing out the errors.
STATUS
approved