A134646 Number of n X n (0,1,2)-matrices with every row sum 3 and column sum 3.

0, 2, 31, 1344, 111920, 16214000, 3758757240, 1310799454720, 655551508577280, 452647176631372800, 418399785559398720000, 504669505260741099417600, 777461035821119354357452800, 1501959201213688265322501427200

Offset

1,2

References

Zhonghua Tan, Shanzhen Gao, Kenneth Mathies, Joshua Fallon, Counting (0,1,2)-Matrices, Congressus Numeratium, December 2008.

Links

R. H. Hardin, Table of n, a(n) for n=1..99

Formula

a(n) = Sum_{alpha = 0 .. n} Sum_{beta = 0 .. n-alpha } (-4)^(n - alpha - beta) * 3^beta * n!^2 * (beta + 3*alpha)! / (alpha!^2 * beta! * (n - alpha - beta)! * 6^(n + alpha)).

a(n) ~ sqrt(Pi) * 3^(n + 1/2) * n^(3*n + 1/2) / (2^(2*n - 1/2) * exp(3*n-2)). - Vaclav Kotesovec, Oct 21 2023

Example

a(2) = 2:
21 12
12 21

Mathematica

Table[Sum[Sum[(-4)^(n - alpha - beta) * 3^beta * n!^2 * (beta + 3*alpha)! / (alpha!^2 * beta! * (n - alpha - beta)! * 6^(n + alpha)), {beta, 0, n - alpha}], {alpha, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)

Crossrefs

Cf. A000681, A134645.

Sequence in context: A246970 A246969 A358567 * A368354 A197320 A239332

Adjacent sequences: A134643 A134644 A134645 * A134647 A134648 A134649

Keyword

nonn,easy

Author

Shanzhen Gao, Nov 05 2007

Extensions

Definition corrected and a(7) and a(8) found (by direct enumeration) by R. H. Hardin, Oct 18 2009

a(9) - a(99) from R. H. Hardin Feb 06 2010

Status

approved