

A134648


Number of 2n X n (0,1)matrices with row sums 2 and column sums 4.


4



0, 1, 90, 44730, 56586600, 154700988750, 807998767676100, 7373018003758407000, 109829050417159537464000, 2532230252503738514963235000, 86574740102712303011539719750000, 4237239732072431006302896746240010000
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OFFSET

1,3


COMMENTS

t(m,n) in the formula gives the number of (0,1)matrices of size m*n with row sum 4 and column sum 2. a(n) in the formula gives the number of (0,1)matrices of size n*(2n) with row sum 4 and column sum 2.  Shanzhen Gao, Feb 16 2010


REFERENCES

Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)matrices with row sum two and some constant column sums. In Proceedings of the FortyFirst Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 4553.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..49


FORMULA

t(m,n) = (1/24^m)*Sum_{j=0..m} Sum_{k=0..mj} ((1)^(mjk)*3^j*6^(mjk)m!n!(4k+2(mjk))!/(j!k!(mjk)!(2k+(mjk))!*2^(2k+(mjk)))).
a(n) = (1/24^n)*Sum_{j=0..n} Sum_{k=0..nj} ((1)^(njk)*3^j*6^(njk)*n!(2n)!(2n2j+2k)!/(j!k!(njk)!(nj+k)!*2^(nj+k))).  Shanzhen Gao, Feb 16 2010


EXAMPLE

Number of 4 X 2 (0,1)matrices: 1;
Number of 6 X 3 (0,1)matrices: 90;
Number of 8 X 4 (0,1)matrices: 44730;
Number of 10 X 5 (0,1)matrices: 5658660.


CROSSREFS

Cf. A132202, A134646, A000681, A000986, A134645, A139670, etc.
Sequence in context: A323317 A246634 A270508 * A145413 A279442 A172572
Adjacent sequences: A134645 A134646 A134647 * A134649 A134650 A134651


KEYWORD

nonn


AUTHOR

Shanzhen Gao, Nov 05 2007


EXTENSIONS

a(7) onwards from R. H. Hardin, Oct 18 2009


STATUS

approved



