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A134646 Number of n X n (0,1,2)-matrices with every row sum 3 and column sum 3. 3
0, 2, 31, 1344, 111920, 16214000, 3758757240, 1310799454720, 655551508577280, 452647176631372800, 418399785559398720000, 504669505260741099417600, 777461035821119354357452800, 1501959201213688265322501427200 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Zhonghua Tan, Shanzhen Gao, Kenneth Mathies, Joshua Fallon, Counting (0,1,2)-Matrices, Congressus Numeratium, December 2008.
LINKS
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
Sequence in context: A246970 A246969 A358567 * A368354 A197320 A239332
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

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Last modified February 23 20:31 EST 2024. Contains 370288 sequences. (Running on oeis4.)