A204102 - OEIS

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.

%I #11 Mar 03 2018 05:35:22

%S 2304,31104,419904,5738688,78428736,1073134656,14683622976,

%T 200937920832,2749733365824,37629117912384,514941023905344,

%U 7046791236157248,96432920316542016,1319651562497299776,18058980695442371136

%N 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.

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

%H R. H. Hardin, <a href="/A204102/b204102.txt">Table of n, a(n) for n = 1..210</a>

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

%F 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

%e Some solutions for n=5:

%e 0 2 0 1 2 2 2 1 2 0 2 2 0 0 2 2 0 0 0 2

%e 0 1 0 1 0 1 0 1 2 0 1 1 1 1 2 2 1 1 1 1

%e 2 1 2 2 0 1 2 1 2 0 2 2 0 0 0 2 0 2 2 2

%e 2 0 0 1 1 1 2 1 2 1 1 1 1 1 2 2 0 1 0 1

%e 1 1 2 2 0 1 0 0 2 1 2 2 2 0 2 1 0 1 2 1

%e 0 0 0 1 0 2 2 1 2 1 0 0 1 0 1 1 2 1 2 0

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 10 2012