A341097 Number of partitions of n into 9 distinct squarefree parts.

1, 1, 1, 1, 3, 2, 3, 3, 7, 7, 8, 10, 16, 18, 18, 22, 33, 35, 39, 47, 65, 69, 77, 89, 117, 126, 138, 163, 205, 223, 242, 282, 344, 376, 407, 466, 561, 612, 664, 751, 889, 966, 1047, 1176, 1365, 1488, 1606, 1792, 2056, 2240, 2406, 2672, 3032, 3286, 3532, 3891

Offset

58,5

Links

Table of n, a(n) for n=58..113.

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, 9):
seq(a(n), n=58..113);  # 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, 9];
Table[a[n], {n, 58, 113}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326522, A341069, A341073, A341074, A341075, A341095, A341096, A341098.

Sequence in context: A117231 A106151 A323467 * A239959 A214435 A215926

Adjacent sequences: A341094 A341095 A341096 * A341098 A341099 A341100

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved