A341096 Number of partitions of n into 8 distinct squarefree parts.

1, 0, 1, 2, 2, 1, 3, 4, 5, 5, 8, 12, 14, 13, 18, 24, 28, 27, 38, 49, 55, 57, 71, 89, 99, 104, 125, 156, 171, 183, 217, 259, 285, 303, 353, 416, 457, 486, 559, 653, 710, 758, 858, 992, 1073, 1148, 1284, 1468, 1591, 1693, 1881, 2128, 2296, 2438, 2694, 3018, 3251, 3455, 3783, 4218, 4522

Offset

45,4

Links

Table of n, a(n) for n=45..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`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 8):
seq(a(n), n=45..105);  # Alois P. Heinz, Feb 04 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[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
a[n_] := b[n, n, 8];
Table[a[n], {n, 45, 105}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326443, A341068, A341073, A341074, A341075, A341095, A341097, A341098.

Sequence in context: A286548 A256134 A091971 * A065185 A289412 A266504

Adjacent sequences: A341093 A341094 A341095 * A341097 A341098 A341099

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved