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A341095 Number of partitions of n into 7 distinct squarefree parts.

%I A341095 #9 Feb 24 2022 07:17:09
%S A341095 1,1,0,1,2,2,2,4,6,7,7,10,14,15,15,21,28,32,32,44,53,60,60,76,93,103,
%T A341095 107,131,157,172,178,211,247,273,283,333,384,423,439,507,577,629,657,
%U A341095 747,846,917,960,1078,1211,1306,1362,1521,1691,1822,1898,2103,2322,2494,2596,2850,3134
%N A341095 Number of partitions of n into 7 distinct squarefree parts.
%p A341095 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341095       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341095       `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341095     end:
%p A341095 a:= n-> b(n$2, 7):
%p A341095 seq(a(n), n=34..94);  # _Alois P. Heinz_, Feb 04 2021
%t A341095 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341095      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341095      If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341095 a[n_] := b[n, n, 7];
%t A341095 Table[a[n], {n, 34, 94}] (* _Jean-François Alcover_, Feb 24 2022, after _Alois P. Heinz_ *)
%Y A341095 Cf. A005117, A008966, A098236, A307835, A308952, A341067, A341073, A341074, A341075, A341096, A341097, A341098.
%K A341095 nonn
%O A341095 34,5
%A A341095 _Ilya Gutkovskiy_, Feb 04 2021