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A116449
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Number of partitions of n into an equal number of prime and composite parts.
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3
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1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 4, 3, 4, 4, 6, 6, 11, 11, 13, 17, 20, 26, 32, 37, 43, 55, 63, 81, 92, 111, 126, 159, 183, 225, 259, 307, 357, 430, 497, 589, 683, 797, 929, 1093, 1270, 1478, 1712, 1979, 2303, 2665, 3086, 3556, 4102, 4716, 5444, 6256, 7194, 8243, 9456, 10824
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OFFSET
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0,10
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COMMENTS
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a(n) = A002865(n) - A116450(n).
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..1000
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EXAMPLE
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a(14) = #{2+2*2*3, (2+2)+(2*3+2*2), 5+3*3, (3+3)+(2*2+2*2)} =
4;
a(15) = #{3+2*2*3, 5+2*5, (2+3)+(2*2+2*3), 7+2*2*2,
(2+5)+(2*2+2*2), 11+2*2} = 6.
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MATHEMATICA
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terms = 61;
pp = 1/(Product[1 - If[PrimeQ[k], y, 1/y]*x^k, {k, 2, terms-3}] + O[x]^terms) // Normal;
Take[Expand[pp ], terms-5] // CoefficientList[#, x]& (* Jean-François Alcover, Dec 30 2017, after Andrew Howroyd *)
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PROG
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(PARI)
parts(n)={1/(prod(k=2, n, 1 - if(isprime(k), y, 1/y)*x^k + O(x*x^n)))}
{my(n=60); apply(p->polcoeff(p, 0), Vec(parts(n)))} \\ Andrew Howroyd, Dec 29 2017
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CROSSREFS
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Sequence in context: A093779 A231898 A276638 * A316433 A071046 A324757
Adjacent sequences: A116446 A116447 A116448 * A116450 A116451 A116452
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Feb 16 2006
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EXTENSIONS
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a(0)=1 from Andrew Howroyd, Dec 29 2017
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STATUS
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approved
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