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A052284 Number of compositions of n into nonprime numbers. 17
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 (list; graph; refs; listen; history; text; internal format)
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).

Cf. A000041 & A023360.

Column k=0 of A224344.

Sequence in context: A072465 A204631 A323361 * A133670 A127272 A238528

Adjacent sequences:  A052281 A052282 A052283 * A052285 A052286 A052287

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

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)