A341466 Number of partitions of n into 7 distinct nonprime parts.

1, 0, 1, 1, 2, 2, 4, 3, 6, 6, 9, 9, 14, 15, 21, 23, 30, 33, 43, 47, 61, 67, 81, 91, 112, 123, 150, 165, 194, 217, 255, 281, 330, 363, 417, 461, 529, 582, 665, 730, 823, 905, 1018, 1115, 1253, 1368, 1519, 1662, 1844, 2010, 2227, 2419, 2659, 2894, 3175, 3442

Offset

50,5

Links

Table of n, a(n) for n=50..105.

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, 7):
seq(a(n), n=50..105);  # 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, 7];
Table[a[n], {n, 50, 105}] (* Jean-François Alcover, Feb 23 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005171, A018252, A096258, A219201, A302479, A341454, A341461, A341462, A341464, A341465, A341467.

Sequence in context: A090105 A082146 A037145 * A357709 A238790 A238787

Adjacent sequences: A341463 A341464 A341465 * A341467 A341468 A341469

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved