|
%I #21 Aug 19 2018 03:23:37
%S 1,24,997,51264,2940841,180296088,11559133741,765337680384,
%T 51921457661905,3590122671128664,252070718210663749,
%U 17922684123178825536,1287832671004683373753,93368940577497932331288,6821632357294515590873917,501741975445243527381995520,37121266623211130111114816929
%N Number of singular vector tuples for a general 4-dimensional n X n X n X n tensor.
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/svt.html">On the Number of Singular Vector Tuples of Hyper-Cubical Tensors</a>, 2016.
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="https://arxiv.org/abs/1605.00172">On the number of Singular Vector Tuples of Hyper-Cubical Tensors</a>, arXiv preprint arXiv:1605.00172 [math.CO], 2016.
%t a[n_] := Module[{a, b, c, d, s}, s = Series[(
%t ((a + b + c)^n - d^n)*
%t ((b + c + d)^n - a^n)*
%t ((c + d + a)^n - b^n)*
%t ((d + a + b)^n - c^n))/(
%t (a + b + c - d)*
%t (b + c + d - a)*
%t (c + d + a - b)*
%t (d + a + b - c)),
%t {a, 0, n}, {b, 0, n}, {c, 0, n}, {d, 0, n}] // Normal // Expand;
%t Cases[List @@ s, k_Integer a^(n-1) b^(n-1) c^(n-1) d^(n-1)] /. (a|b|c|d) -> 1 // First
%t ];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 17}] (* _Jean-François Alcover_, Aug 19 2018, after A271905 *)
%Y See A271905 for the three-dimensional analog.
%Y Column k=4 of A284308.
%K nonn
%O 1,2
%A _Doron Zeilberger_, May 02 2016
|
