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

5,9

Links

Table of n, a(n) for n=5..68.

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 *)

Crossrefs

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

Sequence in context: A123576 A094824 A029054 * A008997 A341453 A341454

Adjacent sequences: A341449 A341450 A341451 * A341453 A341454 A341455

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved