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.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 13, 25, 56, 110, 218, 494, 1216, 2702, 6477, 14752, 35758, 83730, 208107, 499459, 1250815, 3048590, 7787399, 19260830, 49686365, 124430675, 324018684, 820906005, 2155194085, 5514650519, 14578030389, 37630395887, 100201473164

Offset

0,10

Links

Table of n, a(n) for n=0..37.

Formula

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

Maple

b:= proc(n, i) option remember; (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)
    end:
a:= n-> b(1, n):
seq(a(n), n=0..33);  # Alois P. Heinz, Jan 30 2024

Crossrefs

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

Sequence in context: A048871 A324702 A072921 * A289529 A087250 A065301

Adjacent sequences: A369711 A369712 A369713 * A369715 A369716 A369717

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2024

Extensions

a(34)-a(37) from Alois P. Heinz, Jan 30 2024

Status

approved