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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
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-François 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
KEYWORD
nonn
AUTHOR
Doron Zeilberger, May 02 2016
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)