A204102 Number of (n+1) X 5 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that b(i,j)*b(i-1,j)-c(i,j)*c(i,j-1) is nonzero.

2304, 31104, 419904, 5738688, 78428736, 1073134656, 14683622976, 200937920832, 2749733365824, 37629117912384, 514941023905344, 7046791236157248, 96432920316542016, 1319651562497299776, 18058980695442371136

Offset: 1

Author

R. H. Hardin, Jan 10 2012

Keywords

• nonn

Comments

Also 0..2 arrays with no 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

Examples

			Some solutions for n=5:
  0 2 0 1 2    2 2 1 2 0    2 2 0 0 2    2 0 0 0 2
  0 1 0 1 0    1 0 1 2 0    1 1 1 1 2    2 1 1 1 1
  2 1 2 2 0    1 2 1 2 0    2 2 0 0 0    2 0 2 2 2
  2 0 0 1 1    1 2 1 2 1    1 1 1 1 2    2 0 1 0 1
  1 1 2 2 0    1 0 0 2 1    2 2 2 0 2    1 0 1 2 1
  0 0 0 1 0    2 2 1 2 1    0 0 1 0 1    1 2 1 2 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 15*a(n-1) - 270*a(n-3) + 324*a(n-4).

Empirical g.f.: 576*x*(4 - 6*x - 81*x^2 + 108*x^3) / ((1 - 15*x + 18*x^2)*(1 - 18*x^2)). - Colin Barker, Mar 03 2018