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A132202 Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3. 3
1, 1860, 90291600, 31082452632000, 46764764308702440000, 229747284991066934931840000, 3031982831164890119435183865600000, 93453554057243260025029337978773248000000, 6055976192395031960092036887782708145734400000000, 760152286561053082358524425840024164536832608896000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..10.

FORMULA

a(M,N)=2^(-M)*sum_{i=0..N} {(-1)^{i}M!N!(2M-2i)!}/{i!(M-i)!(N-i)!6^{N-i}}, for M=3n, N=2n.

EXAMPLE

1 for 3X2:

11

11

11

1860 for 6X4.

90291600 for 9X6.

MAPLE

f:=proc(m, n) 2^(-m)*add( ((-1)^(i)*m!*n!*(2*m-2*i)!)/ (i!*(m-i)!*(n-i)!*6^(n-i)), i=0..n); end;

[seq(f(3*n, 2*n), n=0..10)];

CROSSREFS

Cf. A134772, A134648.

Sequence in context: A213868 A022062 A107526 * A054815 A295995 A237257

Adjacent sequences:  A132199 A132200 A132201 * A132203 A132204 A132205

KEYWORD

nonn,easy

AUTHOR

Shanzhen Gao, Nov 05 2007

EXTENSIONS

Edited and extended with Maple code by R. H. Hardin and N. J. A. Sloane, Oct 18 2009

STATUS

approved

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Last modified August 10 08:49 EDT 2022. Contains 356039 sequences. (Running on oeis4.)