A341073 Number of partitions of n into 4 distinct squarefree parts.

1, 1, 1, 1, 2, 4, 3, 2, 5, 7, 8, 7, 11, 13, 15, 13, 17, 20, 23, 21, 28, 33, 34, 32, 40, 44, 47, 44, 55, 63, 66, 62, 75, 84, 87, 81, 98, 110, 115, 109, 127, 144, 148, 140, 159, 180, 186, 177, 199, 220, 231, 217, 241, 264, 275, 262, 290, 317, 325, 314, 343, 376, 382, 368, 403

Offset

11,5

Links

Alois P. Heinz, Table of n, a(n) for n = 11..10000

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, 4):
seq(a(n), n=11..75);  # 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, 4];
Table[a[n], {n, 11, 75}] (* Jean-François Alcover, Jul 14 2021, after Alois P. Heinz *)

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308767, A341064, A341074, A341075, A341095, A341096, A341097, A341098.

Sequence in context: A320044 A329876 A128868 * A095986 A212637 A283273

Adjacent sequences: A341070 A341071 A341072 * A341074 A341075 A341076

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved