A341460 Number of partitions of n into 10 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, 68, 79, 92, 104, 122, 139, 157, 181, 208, 234, 270, 304, 347, 391, 445, 499, 569, 636, 724, 805, 913, 1015, 1150, 1274, 1440, 1592, 1796, 1980, 2231, 2455

Offset: 10

Author

Ilya Gutkovskiy, Feb 12 2021

Keywords

• nonn

Crossrefs

Cf. A002095, A005171, A018252, A062610, A259201, A341408, A341451, A341452, 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, 10):
seq(a(n), n=10..69);  # 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, 10];
Table[a[n], {n, 10, 69}] (* Jean-François Alcover, Feb 28 2022, after Alois P. Heinz *)
Table[Count[IntegerPartitions[n,{10}],?(NoneTrue[#,PrimeQ]&)],{n,10,70}] (* _Harvey P. Dale, Sep 01 2024 *)