A341457 Number of partitions of n into 9 nonprime parts.

1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 6, 6, 7, 9, 10, 12, 15, 17, 20, 24, 28, 32, 38, 44, 51, 60, 67, 79, 91, 104, 120, 138, 154, 180, 203, 232, 262, 300, 335, 385, 428, 489, 543, 620, 688, 782, 861, 979, 1078, 1222, 1341, 1518, 1661, 1875, 2048, 2308

Offset: 9

Author

Ilya Gutkovskiy, Feb 12 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..10000

Crossrefs

Cf. A002095, A005171, A018252, A062610, A259200, A341408, A341451, A341452, A341453, A341454, A341455.

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, 9):
seq(a(n), n=9..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], 0]]];
a[n_] := b[n, n, 9];
Table[a[n], {n, 9, 68}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)