A172544 Number of n X n 0..1 arrays with row sums 6 and column sums 6.

0, 0, 0, 0, 0, 1, 5040, 187530840, 12025780892160, 1289144584143523800, 226885231700215713535680, 64051375889927380035549804336, 28278447454165011203551734584421120

Offset: 1

Author

R. H. Hardin Feb 06 2010

Keywords

• nonn

Comments

Also number of ways to arrange 6n rooks on an n X n chessboard, with no more than 6 rooks in each row and column. - Vaclav Kotesovec, Aug 04 2013

Generally (Canfield + McKay, 2004), a(n) ~ exp(-1/2)*binomial(n,s)^(2*n) / binomial(n^2,s*n), or a(n) ~ sqrt(2*Pi)*exp(-n*s-1/2*(s-1)^2)*(n*s)^(n*s+1/2)*(s!)^(-2*n). - Vaclav Kotesovec, Aug 04 2013

Links

• R. H. Hardin, Table of n, a(n) for n=1..28
• E. R. Canfield and B. D. McKay, Asymptotic enumeration of dense 0-1 matrices with equal row and column sums, Electron. J. Combin. 12 (2005)
• Shalosh B. Ekhad and Doron Zeilberger, In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married, if Each Person Has Exactly k Spouses

Crossrefs

Column 6 of A008300.

Formula

From Vaclav Kotesovec, Aug 04 2013: (Start)

a(n) ~ exp(-1/2)*binomial(n,6)^(2*n)/binomial(n^2,6*n), (Canfield + McKay, 2004)

a(n) ~ sqrt(Pi)*2^(1-2*n)*3^(2*n+1/2)*5^(-2*n)*exp(-6*n-25/2)*n^(6*n+1/2)

(End)