A341095 Number of partitions of n into 7 distinct squarefree parts.

1, 1, 0, 1, 2, 2, 2, 4, 6, 7, 7, 10, 14, 15, 15, 21, 28, 32, 32, 44, 53, 60, 60, 76, 93, 103, 107, 131, 157, 172, 178, 211, 247, 273, 283, 333, 384, 423, 439, 507, 577, 629, 657, 747, 846, 917, 960, 1078, 1211, 1306, 1362, 1521, 1691, 1822, 1898, 2103, 2322, 2494, 2596, 2850, 3134

Offset

34,5

Links

Table of n, a(n) for n=34..94.

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, 7):
seq(a(n), n=34..94);  # 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, 7];
Table[a[n], {n, 34, 94}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308952, A341067, A341073, A341074, A341075, A341096, A341097, A341098.

Sequence in context: A265251 A336032 A093393 * A090858 A187504 A036654

Adjacent sequences: A341092 A341093 A341094 * A341096 A341097 A341098

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved