A332002 - OEIS

%I #12 Nov 26 2020 12:15:08

%S 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 3452,108,1632,132,30460,8,55740,376,3872,352,18864,132,315972,1266,

%U 13368,352,958264,108,1621272,2228,10176,6166,4957876,352,2902866,2132

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

%H Alois P. Heinz, <a href="/A332002/b332002.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%e a(9) = 6 because we have [8, 1], [7, 2], [5, 4], [4, 5], [2, 7] and [1, 8].

%p a:= proc(n) local b; b:=

%p       proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<1, 0,

%p         b(m, i-1, p)+`if`(i>m or igcd(i, n)>1, 0, b(m-i, i-1, p+1))))

%p       end; forget(b): b(n$2, 0)

%p     end:

%p seq(a(n), n=0..63);  # _Alois P. Heinz_, Feb 04 2020

%t 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 a /@ Range[0, 63] (* _Jean-François Alcover_, Nov 26 2020, after _Alois P. Heinz_ *)

%Y Cf. A032020, A036998, A057562, A100347, A331888, A332003.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Feb 04 2020