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A341096 Number of partitions of n into 8 distinct squarefree parts.

%I A341096 #9 Feb 24 2022 07:17:22
%S A341096 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,
%T A341096 125,156,171,183,217,259,285,303,353,416,457,486,559,653,710,758,858,
%U A341096 992,1073,1148,1284,1468,1591,1693,1881,2128,2296,2438,2694,3018,3251,3455,3783,4218,4522
%N A341096 Number of partitions of n into 8 distinct squarefree parts.
%p A341096 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341096       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341096       `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341096     end:
%p A341096 a:= n-> b(n$2, 8):
%p A341096 seq(a(n), n=45..105);  # _Alois P. Heinz_, Feb 04 2021
%t A341096 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341096      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341096      If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341096 a[n_] := b[n, n, 8];
%t A341096 Table[a[n], {n, 45, 105}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y A341096 Cf. A005117, A008966, A098236, A307835, A326443, A341068, A341073, A341074, A341075, A341095, A341097, A341098.
%K A341096 nonn
%O A341096 45,4
%A A341096 _Ilya Gutkovskiy_, Feb 04 2021