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A247158 Number of binary n X n matrices in which each row or column sum is at most n/2. 10

%I #46 Jun 01 2017 03:03:01

%S 1,1,7,34,7343,304186,1709852332,702998475376,94473463102448047,

%T 417235486592360297626,1273060578884483984898786092,

%U 63478599188626680785194983697744,4243780803142765740205701619107014789924

%N Number of binary n X n matrices in which each row or column sum is at most n/2.

%H Andrew Howroyd, <a href="/A247158/b247158.txt">Table of n, a(n) for n = 0..15</a>

%H R. J. Mathar, <a href="/A247158/a247158.pdf">The number of binary nXm matrices with at most k 1's in each row or column</a>

%H E. Ordentlich, F. Parvaresh, R. M. Roth, <a href="http://dx.doi.org/10.1137/110857465">Asymptotic enumeration of binary matrices with bounded row and column sums</a>, SIAM J. Discrete Math. 26 (4) (2012) 1550-1575.

%H E. Ordentlich, F. Parvaresh, R. M. Roth, <a href="http://www.hpl.hp.com/techreports/2011/HPL-2011-239.pdf">Asymptotic enumeration of binary matrices with bounded row and column weights</a>, HPL-2011-239.

%e 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.

%Y Cf. A197458, A283500.

%K nonn

%O 0,3

%A _R. J. Mathar_, Nov 21 2014

%E a(6)-a(9) from _Hiroaki Yamanouchi_, Nov 22 2014

%E a(10)-a(11) from _Hiroaki Yamanouchi_, Nov 26 2014

%E a(12) from _Andrew Howroyd_, May 31 2017

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)