cp's OEIS Frontend

A331845 Number of compositions (ordered partitions) of n into distinct cubes.

%I A331845 #13 Oct 31 2020 12:45:58
%S A331845 1,1,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,
%T A331845 0,2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,
%U A331845 0,0,0,0,2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,6,0,0,0,0,0,0,6,24
%N A331845 Number of compositions (ordered partitions) of n into distinct cubes.
%H A331845 Alois P. Heinz, <a href="/A331845/b331845.txt">Table of n, a(n) for n = 0..65536</a>
%H A331845 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A331845 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A331845 a(36) = 6 because we have [27,8,1], [27,1,8], [8,27,1], [8,1,27], [1,27,8] and [1,8,27].
%p A331845 b:= proc(n, i, p) option remember;
%p A331845       `if`((i*(i+1)/2)^2<n, 0, `if`(n=0, p!,
%p A331845       `if`(i^3>n, 0, b(n-i^3, i-1, p+1))+b(n, i-1, p)))
%p A331845     end:
%p A331845 a:= n-> b(n, iroot(n, 3), 0):
%p A331845 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jan 30 2020
%t A331845 b[n_, i_, p_] := b[n, i, p] = If[(i(i+1)/2)^2 < n, 0, If[n == 0, p!, If[i^3 > n, 0, b[n-i^3, i-1, p+1]] + b[n, i-1, p]]];
%t A331845 a[n_] := b[n, Floor[n^(1/3)], 0];
%t A331845 a /@ Range[0, 100] (* _Jean-François Alcover_, Oct 31 2020, after _Alois P. Heinz_ *)
%Y A331845 Cf. A000578, A023358, A032020, A032021, A032022, A218396, A219107, A279329, A331843, A331844, A331846, A331847.
%K A331845 nonn,look
%O A331845 0,10
%A A331845 _Ilya Gutkovskiy_, Jan 29 2020