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A341098
Number of partitions of n into 10 distinct squarefree parts.
6
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
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2021
STATUS
approved