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A272551 Number of singular vector tuples for a general 4-dimensional n X n X n X n tensor. 5
1, 24, 997, 51264, 2940841, 180296088, 11559133741, 765337680384, 51921457661905, 3590122671128664, 252070718210663749, 17922684123178825536, 1287832671004683373753, 93368940577497932331288, 6821632357294515590873917, 501741975445243527381995520, 37121266623211130111114816929 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..17.

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.

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-Fran├žois Alcover, Aug 19 2018, after A271905 *)

CROSSREFS

See A271905 for the three-dimensional analog.

Column k=4 of A284308.

Sequence in context: A058810 A265872 A223147 * A222933 A222384 A129622

Adjacent sequences:  A272548 A272549 A272550 * A272552 A272553 A272554

KEYWORD

nonn

AUTHOR

Doron Zeilberger, May 02 2016

STATUS

approved

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Last modified May 30 12:03 EDT 2020. Contains 334724 sequences. (Running on oeis4.)