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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 (list; graph; refs; listen; history; text; internal format)
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 Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.

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..m-j} ((-1)^(m-j-k)*3^j*6^(m-j-k)m!n!(4k+2(m-j-k))!/(j!k!(m-j-k)!(2k+(m-j-k))!*2^(2k+(m-j-k)))).

a(n) = (1/24^n)*Sum_{j=0..n} Sum_{k=0..n-j} ((-1)^(n-j-k)*3^j*6^(n-j-k)*n!(2n)!(2n-2j+2k)!/(j!k!(n-j-k)!(n-j+k)!*2^(n-j+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

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)