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A341097 Number of partitions of n into 9 distinct squarefree parts.

%I A341097 #9 Feb 24 2022 07:25:29
%S A341097 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,
%T A341097 138,163,205,223,242,282,344,376,407,466,561,612,664,751,889,966,1047,
%U A341097 1176,1365,1488,1606,1792,2056,2240,2406,2672,3032,3286,3532,3891
%N A341097 Number of partitions of n into 9 distinct squarefree parts.
%p A341097 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341097       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341097       `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341097     end:
%p A341097 a:= n-> b(n$2, 9):
%p A341097 seq(a(n), n=58..113);  # _Alois P. Heinz_, Feb 04 2021
%t A341097 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341097      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341097      If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341097 a[n_] := b[n, n, 9];
%t A341097 Table[a[n], {n, 58, 113}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y A341097 Cf. A005117, A008966, A098236, A307835, A326522, A341069, A341073, A341074, A341075, A341095, A341096, A341098.
%K A341097 nonn
%O A341097 58,5
%A A341097 _Ilya Gutkovskiy_, Feb 04 2021