A341455 Number of partitions of n into 8 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, 43, 51, 59, 67, 77, 90, 101, 119, 133, 152, 172, 199, 220, 256, 283, 325, 359, 412, 453, 520, 569, 652, 711, 810, 882, 1005, 1091, 1238, 1341, 1519, 1641, 1854, 1999

Offset

8,9

Links

Table of n, a(n) for n=8..67.

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, 8):
seq(a(n), n=8..67);  # 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, 8];
Table[a[n], {n, 8, 67}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)

Crossrefs

Cf. A002095, A005171, A018252, A062610, A259198, A341408, A341451, A341452, A341453, A341454, A341457.

Sequence in context: A008997 A341453 A341454 * A341457 A341460 A005851

Adjacent sequences: A341452 A341453 A341454 * A341456 A341457 A341458

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved