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A134645
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Number of 2n X 3n (0,1,2)-matrices with every row sum 3 and column sum 2.
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2
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7, 16260, 747558000, 250071339672000, 369820640830881240000, 1796185853884657144990080000, 23511842995969107700302647865600000, 720289186703359375552628986978410240000000, 46455761324619133018320834819622638940550400000000, 5809177204262302555518772962193269714031251010176000000000
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OFFSET
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1,1
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REFERENCES
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Zhonghua Tan, Shanzhen Gao, Kenneth Mathies, Joshua Fallon, Counting (0,1,2)-Matrices, Congressus Numeratium, December 2008.
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LINKS
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Table of n, a(n) for n=1..10.
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FORMULA
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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).
a(n) = (3n)!(2n)!288^(-n) * Sum_{i=0..2n} (6n-2i)!6^i/(i!(3n-i)!(2n-i)!). - Shanzhen Gao, Mar 02 2010
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EXAMPLE
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a(1) = 7:
111 210 (6 ways)
111 012
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MAPLE
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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;
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CROSSREFS
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Cf. A000681, A134646.
Sequence in context: A344532 A280813 A203685 * A327840 A115997 A013786
Adjacent sequences: A134642 A134643 A134644 * A134646 A134647 A134648
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KEYWORD
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nonn
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AUTHOR
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Shanzhen Gao, Nov 05 2007
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EXTENSIONS
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Corrected, edited and extended with Maple program by R. H. Hardin and N. J. A. Sloane, Oct 18 2009
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STATUS
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approved
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