A247158 Number of binary n X n matrices in which each row or column sum is at most n/2.
1, 1, 7, 34, 7343, 304186, 1709852332, 702998475376, 94473463102448047, 417235486592360297626, 1273060578884483984898786092, 63478599188626680785194983697744, 4243780803142765740205701619107014789924
Offset: 0
Keywords
Examples
a(2)=7 counts the following 2 X 2 matrices: 1 matrix with all zeros, 4 matrices where a 1 is at any of the four corners, and 2 matrices with 1's covering a diagonal.
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..15
- R. J. Mathar, The number of binary nXm matrices with at most k 1's in each row or column
- E. Ordentlich, F. Parvaresh, R. M. Roth, Asymptotic enumeration of binary matrices with bounded row and column sums, SIAM J. Discrete Math. 26 (4) (2012) 1550-1575.
- E. Ordentlich, F. Parvaresh, R. M. Roth, Asymptotic enumeration of binary matrices with bounded row and column weights, HPL-2011-239.
Extensions
a(6)-a(9) from Hiroaki Yamanouchi, Nov 22 2014
a(10)-a(11) from Hiroaki Yamanouchi, Nov 26 2014
a(12) from Andrew Howroyd, May 31 2017