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

9,9

Links

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

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 *)

Crossrefs

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

Sequence in context: A341453 A341454 A341455 * A341460 A005851 A369786

Adjacent sequences: A341454 A341455 A341456 * A341458 A341459 A341460

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved