A369437 -id:A369437 - cp's OEIS frontend

A369735 Number of solutions to 1^3k_1 + 2^3k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

0, 1, 1, 1, 1, 1, 3, 4, 6, 15, 28, 56, 125, 287, 646, 1540, 3625, 8484, 21167, 51458, 126342, 323126, 811538, 2052501, 5339265, 13751212, 35589866, 94032931, 246791641, 650227636, 1739032299, 4630165425, 12373805281, 33429284691, 90073865814, 243460560324

Offset: 0

Ilya Gutkovskiy, Jan 30 2024

nonn

Cf. A007576, A063866, A369345, A369437, A369628, A369734.

b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(1, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 30 2024

Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, 1], {n, 0, 33}]

a(n) = [x^1] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

A368478 a(n) = [x^n] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 22, 88, 236, 568, 1147, 1999, 3030, 4333, 4793, 5620, 4628, 9353, 40048, 312436, 1638550, 7894061, 30866741, 105342660, 323671449, 863529149, 2152428536, 4750103818, 9796453345, 18572505806, 32181800057, 55712628236

Offset: 0

Ilya Gutkovskiy, Jan 25 2024

nonn

Cf. A000583, A316706, A369358, A369433, A369437.

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(n$2):
seq(a(n), n=0..33);  # Alois P. Heinz, Jan 25 2024

a(34)-a(38) from Alois P. Heinz, Jan 25 2024

cp's OEIS Frontend

A369735 Number of solutions to 1^3k_1 + 2^3k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

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Formula

A368478 a(n) = [x^n] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

Views

Author

Keywords

Crossrefs

Programs

Maple

Extensions

cp's OEIS Frontend

A369735 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.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Formula

A368478 a(n) = [x^n] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

Views

Author

Keywords

Crossrefs

Programs

Maple

Extensions

A369735 Number of solutions to 1^3k_1 + 2^3k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.