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A332001 Number of compositions (ordered partitions) of n into distinct parts that do not divide n.

%I A332001 #10 Nov 30 2020 18:22:41
%S A332001 1,0,0,0,0,2,0,4,2,4,4,20,2,34,14,20,14,146,8,244,22,140,202,956,16,
%T A332001 782,596,752,216,5786,82,10108,640,4016,5200,6028,218,53674,14570,
%U A332001 19004,980,152810,1786,245884,13588,16534,108382,719156,1494,532532,54316
%N A332001 Number of compositions (ordered partitions) of n into distinct parts that do not divide n.
%H A332001 Alois P. Heinz, <a href="/A332001/b332001.txt">Table of n, a(n) for n = 0..1000</a>
%H A332001 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A332001 a(9) = 4 because we have [7, 2], [5, 4], [4, 5] and [2, 7].
%p A332001 a:= proc(n) local b, l; l, b:= numtheory[divisors](n),
%p A332001       proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<2, 0,
%p A332001         b(m, i-1, p)+`if`(i>m or i in l, 0, b(m-i, i-1, p+1))))
%p A332001       end; forget(b): b(n, n-1, 0)
%p A332001     end:
%p A332001 seq(a(n), n=0..63);  # _Alois P. Heinz_, Feb 04 2020
%t A332001 a[n_] := Module[{b, l = Divisors[n]}, b[m_, i_, p_] := b[m, i, p] = If[m == 0, p!, If[i < 2, 0, b[m, i - 1, p] + If[i > m || MemberQ[l, i], 0, b[m - i, i - 1, p + 1]]]]; b[n, n - 1, 0]];
%t A332001 a /@ Range[0, 63] (* _Jean-François Alcover_, Nov 30 2020, after _Alois P. Heinz_ *)
%Y A332001 Cf. A018818, A032020, A033630, A098743, A100346, A200745, A300702, A331927, A331979.
%K A332001 nonn
%O A332001 0,6
%A A332001 _Ilya Gutkovskiy_, Feb 04 2020