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A332311 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 5.

%I A332311 #11 Nov 17 2020 20:13:05
%S A332311 1,1,1,3,3,4,9,11,11,19,44,31,61,87,117,144,279,311,389,541,640,1003,
%T A332311 1225,2145,2493,3452,3507,5417,6671,8821,11580,17959,21043,26289,
%U A332311 34797,41536,59637,72707,85871,110947,172472,175873,249691,327801,418779,512748
%N A332311 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 5.
%H A332311 Alois P. Heinz, <a href="/A332311/b332311.txt">Table of n, a(n) for n = 0..5000</a>
%H A332311 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A332311 a(6) = 9 because we have [6], [4, 2], [3, 2, 1], [3, 1, 2], [2, 4], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].
%p A332311 b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
%p A332311       p!, add(b(n-i*j, i-1, p+j), j=0..min(irem(i, 5), 1, n/i))))
%p A332311     end:
%p A332311 a:= n-> b(n$2, 0):
%p A332311 seq(a(n), n=0..55);  # _Alois P. Heinz_, Feb 09 2020
%t A332311 b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!, Sum[b[n - i j, i - 1, p + j], {j, 0, Min[Mod[i, 5], 1, n/i]}]]];
%t A332311 a[n_] := b[n, n, 0];
%t A332311 a /@ Range[0, 55] (* _Jean-François Alcover_, Nov 17 2020, after _Alois P. Heinz_ *)
%Y A332311 Cf. A032020, A032021, A035959, A096938, A332309, A332310.
%K A332311 nonn
%O A332311 0,4
%A A332311 _Ilya Gutkovskiy_, Feb 09 2020