A341465 Number of partitions of n into 6 distinct nonprime parts.

1, 0, 1, 1, 2, 2, 4, 3, 6, 5, 8, 10, 13, 13, 18, 20, 26, 30, 36, 40, 49, 55, 65, 76, 88, 97, 114, 128, 146, 167, 187, 209, 237, 262, 294, 331, 366, 405, 449, 496, 547, 608, 663, 730, 798, 875, 953, 1050, 1136, 1239, 1342, 1463, 1577, 1723, 1849, 2008, 2159, 2334

Offset

38,5

Links

Table of n, a(n) for n=38..95.

Maple

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<t 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, 6):
seq(a(n), n=38..95);  # 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], 0]]];
a[n_] := b[n, n, 6];
Table[a[n], {n, 38, 95}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005171, A018252, A096258, A219200, A302479, A341453, A341461, A341462, A341464, A341466, A341467.

Sequence in context: A267451 A062968 A239966 * A304406 A053197 A275234

Adjacent sequences: A341462 A341463 A341464 * A341466 A341467 A341468

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved