0,6

Further terms generated by a Mathematica program written by Gordon G. Cash, who thanks B. R. Perez-Salvador, Universidad Autonoma Metropolitana Unidad Iztapalapa, Mexico, for providing the algorithm on which this program was based.

B. R. Perez-Salvador, S. de los Cobos Silva, M. A. Gutierrez-Andrade and A. Torres-Chazaro, A Reduced Formula for Precise Numbers of (0,1) Matrices in a(R,S), Disc. Math., 2002, 256, 361-372.

Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 12 2006, Table of n, a(n) for n = 0..31

Index entries for sequences related to binary matrices

B. D. McKay, 0-1 matrices with constant row and column sums

a(n)=24^{-n} sum_{alpha +beta + gamma + mu + u =n}frac{3^{ gamma }(-6)^{beta +u }8^{ mu }(n!)^{2}(4alpha +2 gamma + mu )!(beta +2 gamma )!}{alpha!beta! gamma! mu!u!} sum_{i=0}^{ floor (beta +2 gamma )/2 }frac{1}{24^{alpha - gamma +i}2^{beta +2 gamma -i}i!(beta +2 gamma -2i)!(alpha - gamma +i)!} - Shanzhen Gao (sgao2(AT)fau.edu), Nov 07 2007

a(4)=1 because there is only one possible 4 X 4 (0,1) matrix with all row and column sums equal to 4, the matrix of all 1's. a(5)=120=5! because there are 5X4X3X2X1 ways of placing a zero in each successive column (row) so that it is not in the same row (column) as any previously placed.

Cf. A001499, A001501.

Sequence in context: A109897 A074653 A065961 this_sequence A001421 A107446 A159735

Adjacent sequences: A058525 A058526 A058527 this_sequence A058529 A058530 A058531

nonn

David desJardins (david(AT)desjardins.org), Dec 22 2000

More terms from Gordon G. Cash (cash.gordon(AT)epa.gov), Oct 22 2002

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 12 2006