A280285 Number of partitions of n into odd composite numbers (A071904).
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 3, 0, 0, 3, 1, 0, 4, 1, 1, 5, 1, 0, 5, 2, 2, 6, 2, 1, 8, 3, 1, 8, 3, 2, 11, 3, 2, 12, 5, 4, 13, 5, 3, 16, 8, 4, 18, 7, 6, 22, 9, 7, 24, 12, 9, 28, 12, 9, 33, 18, 11, 36, 18, 14, 45, 22, 16, 48, 26, 22, 54, 29, 23, 66, 38
Offset: 0
Keywords
Examples
a(36) = 3 because we have [27, 9], [21, 15] and [9, 9, 9, 9].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Composite Number
- Index entries for related partition-counting sequences
Programs
-
Maple
a:= proc(n) option remember; `if`(n=0, 1, add(add( `if`(d>1 and d::odd and not isprime(d), d, 0), d=numtheory[divisors](j))*a(n-j), j=1..n)/n) end: seq(a(n), n=0..100); # Alois P. Heinz, Dec 31 2016 -
Mathematica
nmax = 100; CoefficientList[Series[(1 - x)/(1 - x^2) Product[(1 - x^(2 k)) (1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: ((1 - x)/(1 - x^2))*Product_{k>=1} (1 - x^(2*k))*(1 - x^prime(k))/(1 - x^k).