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A332002 Number of compositions (ordered partitions) of n into distinct parts all relatively prime to n.

%I A332002 #12 Nov 26 2020 12:15:08
%S A332002 1,1,0,2,2,4,2,12,4,6,4,64,4,132,6,32,32,616,6,1176,32,120,58,4756,32,
%T A332002 3452,108,1632,132,30460,8,55740,376,3872,352,18864,132,315972,1266,
%U A332002 13368,352,958264,108,1621272,2228,10176,6166,4957876,352,2902866,2132
%N A332002 Number of compositions (ordered partitions) of n into distinct parts all relatively prime to n.
%H A332002 Alois P. Heinz, <a href="/A332002/b332002.txt">Table of n, a(n) for n = 0..1000</a>
%H A332002 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A332002 a(9) = 6 because we have [8, 1], [7, 2], [5, 4], [4, 5], [2, 7] and [1, 8].
%p A332002 a:= proc(n) local b; b:=
%p A332002       proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<1, 0,
%p A332002         b(m, i-1, p)+`if`(i>m or igcd(i, n)>1, 0, b(m-i, i-1, p+1))))
%p A332002       end; forget(b): b(n$2, 0)
%p A332002     end:
%p A332002 seq(a(n), n=0..63);  # _Alois P. Heinz_, Feb 04 2020
%t A332002 a[n_] := Module[{b}, b[m_, i_, p_] := b[m, i, p] = If[m == 0, p!, If[i < 1, 0, b[m, i-1, p] + If[i > m || GCD[i, n] > 1, 0, b[m-i, i-1, p+1]]]]; b[n, n, 0]];
%t A332002 a /@ Range[0, 63] (* _Jean-François Alcover_, Nov 26 2020, after _Alois P. Heinz_ *)
%Y A332002 Cf. A032020, A036998, A057562, A100347, A331888, A332003.
%K A332002 nonn
%O A332002 0,4
%A A332002 _Ilya Gutkovskiy_, Feb 04 2020