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A341097
Number of partitions of n into 9 distinct squarefree parts.
6
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
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2021
STATUS
approved