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 A116449 Number of partitions of n into an equal number of prime and composite parts. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS a(n) = A002865(n) - A116450(n). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 EXAMPLE 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A093779 A231898 A276638 * A316433 A071046 A324757 Adjacent sequences:  A116446 A116447 A116448 * A116450 A116451 A116452 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 16 2006 EXTENSIONS a(0)=1 from Andrew Howroyd, Dec 29 2017 STATUS approved

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)