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

72,5

Links

Table of n, a(n) for n=72..126.

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 *)

Crossrefs

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

Sequence in context: A345199 A079159 A192298 * A353330 A254967 A229012

Adjacent sequences: A341095 A341096 A341097 * A341099 A341100 A341101

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved