A272551 Number of singular vector tuples for a general 4-dimensional n X n X n X n tensor.

1, 24, 997, 51264, 2940841, 180296088, 11559133741, 765337680384, 51921457661905, 3590122671128664, 252070718210663749, 17922684123178825536, 1287832671004683373753, 93368940577497932331288, 6821632357294515590873917, 501741975445243527381995520, 37121266623211130111114816929

Offset: 1

Author

Doron Zeilberger, May 02 2016

Keywords

• nonn

Links

• Shalosh B. Ekhad and Doron Zeilberger, On the Number of Singular Vector Tuples of Hyper-Cubical Tensors, 2016.
• Shalosh B. Ekhad and Doron Zeilberger, On the number of Singular Vector Tuples of Hyper-Cubical Tensors, arXiv preprint arXiv:1605.00172 [math.CO], 2016.

Crossrefs

See A271905 for the three-dimensional analog.

Column k=4 of A284308.

Programs

Mathematica

a[n_] := Module[{a, b, c, d, s}, s = Series[(
  ((a + b + c)^n - d^n)*
  ((b + c + d)^n - a^n)*
  ((c + d + a)^n - b^n)*
  ((d + a + b)^n - c^n))/(
  (a + b + c - d)*
  (b + c + d - a)*
  (c + d + a - b)*
  (d + a + b - c)),
  {a, 0, n}, {b, 0, n}, {c, 0, n}, {d, 0, n}] // Normal // Expand;
  Cases[List @@ s, k_Integer a^(n-1) b^(n-1) c^(n-1) d^(n-1)] /. (a|b|c|d) -> 1 // First
];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 17}] (* Jean-François Alcover, Aug 19 2018, after A271905 *)