A341098 Number of partitions of n into 10 distinct squarefree parts.

1, 1, 1, 1, 2, 3, 2, 4, 6, 8, 7, 10, 14, 17, 17, 22, 32, 35, 37, 47, 62, 71, 72, 91, 114, 132, 136, 167, 205, 234, 247, 293, 355, 398, 426, 497, 590, 661, 708, 819, 956, 1066, 1141, 1306, 1501, 1672, 1791, 2030, 2318, 2559, 2747, 3081, 3490, 3835, 4115

Offset: 72

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

• nonn

Crossrefs

Cf. A005117, A008966, A098236, A307835, A326626, A341070, A341073, A341074, A341075, A341095, A341096, A341097.

Programs

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, 10):
seq(a(n), n=72..126);  # 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, 10];
Table[a[n], {n, 72, 126}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)