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
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