A341464 Number of partitions of n into 5 distinct nonprime parts.

1, 1, 1, 1, 2, 2, 4, 4, 5, 7, 7, 9, 12, 14, 15, 19, 21, 27, 29, 35, 38, 47, 49, 59, 65, 77, 82, 96, 102, 119, 128, 147, 157, 181, 189, 216, 231, 260, 276, 309, 327, 366, 387, 431, 454, 505, 529, 584, 617, 678, 713, 780, 818, 892, 938, 1020, 1071, 1164, 1213, 1311, 1378

Offset

28,5

Links

Table of n, a(n) for n=28..88.

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-1), t-1))))
    end:
a:= n-> b(n$2, 5):
seq(a(n), n=28..88);  # 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 - 1], t - 1]]]];
a[n_] := b[n, n, 5];
Table[a[n], {n, 28, 88}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A005171, A018252, A096258, A219199, A302479, A341452, A341461, A341462, A341465, A341466, A341467.

Sequence in context: A266690 A230421 A219641 * A277758 A240027 A203555

Adjacent sequences: A341461 A341462 A341463 * A341465 A341466 A341467

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved