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A134645 Number of 2n X 3n (0,1,2)-matrices with every row sum 3 and column sum 2. 2


%S 7,16260,747558000,250071339672000,369820640830881240000,

%T 1796185853884657144990080000,23511842995969107700302647865600000,

%U 720289186703359375552628986978410240000000,46455761324619133018320834819622638940550400000000,5809177204262302555518772962193269714031251010176000000000

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

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

%F Let t(m,n)=6^{-m} sum_{i=0}^{m}frac{3^{i}m!n!(2n-2i)!}{i!(m-i)!(n-i)!2^{n-i}}; then a(n) = t(2n,3n).

%F a(n) = (3n)!(2n)!288^(-n) * Sum_{i=0..2n} (6n-2i)!6^i/(i!(3n-i)!(2n-i)!). - _Shanzhen Gao_, Mar 02 2010

%e a(1) = 7:

%e 111 210 (6 ways)

%e 111 012

%p f:=proc(m,n) 6^(-m)*add( (3^i*m!*n!*(2*n-2*i)!)/ (i!*(m-i)!*(n-i)!*2^(n-i)), i=0..m); end;

%Y Cf. A000681, A134646.

%K nonn

%O 1,1

%A _Shanzhen Gao_, Nov 05 2007

%E Corrected, edited and extended with Maple program by R. H. Hardin and _N. J. A. Sloane_, Oct 18 2009

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Last modified December 1 17:49 EST 2022. Contains 358475 sequences. (Running on oeis4.)