A341408 Number of partitions of n into 3 nonprime parts.

1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 3, 2, 4, 5, 5, 5, 7, 6, 9, 8, 11, 10, 13, 12, 16, 14, 19, 16, 22, 19, 26, 22, 29, 27, 33, 28, 39, 33, 42, 38, 47, 43, 53, 45, 58, 52, 63, 59, 70, 61, 77, 68, 83, 76, 91, 79, 98, 88, 105, 95, 115, 102, 121, 111, 130, 119, 141, 124, 148

Offset

3,9

Links

Table of n, a(n) for n=3..72.

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, 3):
seq(a(n), n=3..72);  # 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, 3];
a /@ Range[3, 72] (* Jean-François Alcover, Mar 28 2021, after Alois P. Heinz *)

Crossrefs

Cf. A002095, A005171, A018252, A062610, A068307, A341451, A341452, A341453, A341454, A341455, A341457.

Sequence in context: A345901 A305434 A319478 * A104239 A283751 A132321

Adjacent sequences: A341405 A341406 A341407 * A341409 A341410 A341411

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved