cp's OEIS Frontend

A307609 Number of partitions of n^3 into consecutive positive cubes.

%I A307609 #10 Aug 22 2019 20:34:53
%S A307609 1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A307609 1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,
%U A307609 1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A307609 Number of partitions of n^3 into consecutive positive cubes.
%H A307609 Antti Karttunen, <a href="/A307609/b307609.txt">Table of n, a(n) for n = 1..16861</a>
%H A307609 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A307609 a(n) = [x^(n^3)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^3).
%F A307609 a(n) = A297199(A000578(n)).
%F A307609 a(n) >= 2 for n in A097811.
%e A307609 20^3 = 11^3 + 12^3 + 13^3 + 14^3, so a(20) = 2.
%e A307609 2856^3 = 213^3 +...+ 555^3 = 273^3 +...+ 560^3, so a(2856) = 3. See also _Donovan Johnson_'s comment in A097811. - _Antti Karttunen_, Aug 22 2019
%o A307609 (PARI)
%o A307609 A297199(n) = { my(s=0, k=1, c); while((c=k^3) <= n, my(u=n-c, i=k); while(u>0, i++; c = i^3; u=u-c); s += (!u); k++); (s); };
%o A307609 A307609(n) = A297199(n^3); \\ _Antti Karttunen_, Aug 22 2019
%Y A307609 Cf. A000578, A030272, A097811, A131643, A217843, A259792, A297199.
%K A307609 nonn
%O A307609 1,6
%A A307609 _Ilya Gutkovskiy_, Apr 18 2019