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A341096
Number of partitions of n into 8 distinct squarefree parts.
6
1, 0, 1, 2, 2, 1, 3, 4, 5, 5, 8, 12, 14, 13, 18, 24, 28, 27, 38, 49, 55, 57, 71, 89, 99, 104, 125, 156, 171, 183, 217, 259, 285, 303, 353, 416, 457, 486, 559, 653, 710, 758, 858, 992, 1073, 1148, 1284, 1468, 1591, 1693, 1881, 2128, 2296, 2438, 2694, 3018, 3251, 3455, 3783, 4218, 4522
OFFSET
45,4
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, 8):
seq(a(n), n=45..105); # 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, 8];
Table[a[n], {n, 45, 105}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 04 2021
STATUS
approved