A341452 Number of partitions of n into 5 nonprime parts.

1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 6, 7, 9, 9, 12, 14, 16, 18, 22, 24, 29, 31, 38, 40, 49, 50, 62, 65, 77, 81, 97, 98, 120, 122, 144, 149, 176, 178, 212, 214, 251, 255, 299, 304, 352, 355, 412, 417, 482, 485, 559, 564, 643, 650, 742, 745, 850, 856, 965

Offset: 5

Author

Ilya Gutkovskiy, Feb 12 2021

Keywords

• nonn

Crossrefs

Cf. A002095, A005171, A018252, A062610, A259195, A341408, A341451, A341453, A341454, A341455, A341457.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
    end:
a:= n-> b(n$2, 5):
seq(a(n), n=5..68);  # Alois P. Heinz, Feb 12 2021

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
     If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1]]]];
a[n_] := b[n, n, 5];
Table[a[n], {n, 5, 68}] (* Jean-François Alcover, Aug 19 2021, after Alois P. Heinz *)