A341467 Number of partitions of n into 8 distinct nonprime parts.

1, 1, 1, 1, 2, 2, 4, 5, 6, 7, 10, 12, 16, 19, 24, 28, 36, 41, 52, 60, 73, 85, 102, 116, 142, 161, 192, 217, 256, 287, 339, 382, 442, 496, 574, 639, 737, 821, 937, 1041, 1184, 1309, 1483, 1640, 1845, 2037, 2283, 2508, 2807, 3081, 3430, 3761, 4170, 4553, 5045

Offset

64,5

Links

Table of n, a(n) for n=64..118.

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, 8):
seq(a(n), n=64..118);  # 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, 8];
Table[a[n], {n, 64, 118}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005171, A018252, A096258, A219202, A302479, A341455, A341461, A341462, A341464, A341465, A341466.

Sequence in context: A024683 A244017 A339022 * A341468 A071528 A056902

Adjacent sequences: A341464 A341465 A341466 * A341468 A341469 A341470

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved