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%I #15 Nov 09 2020 02:57:29
%S 1,1,1,2,1,3,4,9,9,6,15,17,38,29,53,70,65,91,150,229,277,236,439,489,
%T 514,897,993,1632,1521,2339,2972,3257,4121,5992,5303,7729,10932,15157,
%U 17653,18398,26305,31683,34408,51885,58173,61098,90519,101249,143402,156905
%N Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 3.
%H Alois P. Heinz, <a href="/A332309/b332309.txt">Table of n, a(n) for n = 0..5000</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 b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
%p p!, add(b(n-i*j, i-1, p+j), j=0..min(irem(i, 3), 1, n/i))))
%p end:
%p a:= n-> b(n$2, 0):
%p seq(a(n), n=0..55); # _Alois P. Heinz_, Feb 09 2020
%t 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, 3], 1, n/i]}]]];
%t a[n_] := b[n, n, 0];
%t a /@ Range[0, 55] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)
%Y Cf. A000726, A003105, A032020, A032021, A332310, A332311.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Feb 09 2020
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