This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369714 #28 Jan 27 2025 06:23:02
%S A369714 0,1,1,1,1,1,1,1,1,2,5,13,25,56,110,218,494,1216,2702,6477,14752,
%T A369714 35758,83730,208107,499459,1250815,3048590,7787399,19260830,49686365,
%U A369714 124430675,324018684,820906005,2155194085,5514650519,14578030389,37630395887,100201473164
%N A369714 Number of solutions to 1^4*k_1 + 2^4*k_2 + ... + n^4*k_n = 1, where k_i are from {-1,0,1}, i=1..n.
%F A369714 a(n) = [x^1] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).
%p A369714 b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1, b(n, i-1)+
%p A369714 b(abs(n-i^4), i-1)+b(n+i^4, i-1))))(i*(i+1)*(2*i+1)*(3*i^2+3*i-1)/30)
%p A369714 end:
%p A369714 a:= n-> b(1, n):
%p A369714 seq(a(n), n=0..33); # _Alois P. Heinz_, Jan 30 2024
%t A369714 b[n_, i_] := b[n, i] = Function[m, If[n > m, 0, If[n == m, 1, b[n, i-1] + b[Abs[n-i^4], i-1] + b[n+i^4, i-1]]]][i*(i+1)*(2*i+1)*(3*i^2 + 3*i-1)/30];
%t A369714 a[n_] := b[1, n];
%t A369714 Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Jan 27 2025, after _Alois P. Heinz_ *)
%Y A369714 Cf. A007576, A063866, A368478, A369358, A369628, A369734, A369735.
%K A369714 nonn
%O A369714 0,10
%A A369714 _Ilya Gutkovskiy_, Jan 30 2024
%E A369714 a(34)-a(37) from _Alois P. Heinz_, Jan 30 2024