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A052284
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Number of compositions of n into nonprime numbers.
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4
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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; internal format)
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OFFSET
| 0,5
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COMMENTS
| Starting with offset 1, appears to be row sums of triangle A157424 [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Feb 28 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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FORMULA
| G.f.: 1/( 1 - (Sum_{m nonprime} x^m) ).
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EXAMPLE
| a(6) = 5 because 1+1+1+1+1+1 = 1+1+4 = 1+4+1 = 4+1+1 = 6.
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MATHEMATICA
| nn=50; np=Select[Range[nn], !PrimeQ[ # ] &]; CoefficientList[Series[1/(1-Sum[x^k, {k, np}]), {x, 0, nn}], x] [From T. D. Noe (noe(AT)sspectra.com), Aug 20 2010]
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CROSSREFS
| Cf. A002095 (Number of partitions of n into nonprime parts).
Cf. A000041 & A023360.
Cf. A157424 [From Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Feb 28 2009]
Sequence in context: A002379 A072465 A204631 * A133670 A127272 A113192
Adjacent sequences: A052281 A052282 A052283 * A052285 A052286 A052287
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), May 16 2002
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EXTENSIONS
| Definition and g.f. corrected by N. J. A. Sloane, Aug 19 2010, who thanks Kruchinin Vladimir Victorovich (kru(AT)tcde.ru) for pointing out the errors.
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