Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Jan 30 2024 20:09:42
%S 0,1,1,1,1,1,3,4,6,15,28,56,125,287,646,1540,3625,8484,21167,51458,
%T 126342,323126,811538,2052501,5339265,13751212,35589866,94032931,
%U 246791641,650227636,1739032299,4630165425,12373805281,33429284691,90073865814,243460560324
%N Number of solutions to 1^3*k_1 + 2^3*k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.
%F a(n) = [x^1] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).
%p b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
%p `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
%p end:
%p a:= n-> b(1, n):
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jan 30 2024
%t Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, 1], {n, 0, 33}]
%Y Cf. A007576, A063866, A369345, A369437, A369628, A369734.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Jan 30 2024