%I #24 Jan 30 2024 20:10:30

%S 0,1,1,1,1,1,1,1,1,2,5,13,25,56,110,218,494,1216,2702,6477,14752,

%T 35758,83730,208107,499459,1250815,3048590,7787399,19260830,49686365,

%U 124430675,324018684,820906005,2155194085,5514650519,14578030389,37630395887,100201473164

%N 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 a(n) = [x^1] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

%p b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1, b(n, i-1)+

%p 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 end:

%p a:= n-> b(1, n):

%p seq(a(n), n=0..33); # _Alois P. Heinz_, Jan 30 2024

%Y Cf. A007576, A063866, A368478, A369358, A369628, A369734, A369735.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Jan 30 2024

%E a(34)-a(37) from _Alois P. Heinz_, Jan 30 2024