A204103 Number of (n+1) X 6 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.

9216, 186624, 3779136, 78428736, 1631513664, 34026967296, 710001723456, 14819050600704, 309323110957056, 6456825742349376, 134781435261831744, 2813473850104420416, 58729494893765642496, 1225941854009002910784

Offset

1,1

Comments

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

Links

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

Formula

Empirical: a(n) = 25*a(n-1) -45*a(n-2) -963*a(n-3) +2025*a(n-4) +3645*a(n-5) -6561*a(n-6).

Empirical g.f.: 576*x*(16 - 76*x - 819*x^2 + 2124*x^3 + 3321*x^4 - 6561*x^5) / ((1 - 25*x + 90*x^2 - 81*x^3)*(1 - 45*x^2 - 81*x^3)). - Colin Barker, Jun 06 2018

Example

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

Crossrefs

Sequence in context: A251902 A234139 A175743 * A209595 A223303 A031594

Adjacent sequences: A204100 A204101 A204102 * A204104 A204105 A204106

Keyword

nonn

Author

R. H. Hardin, Jan 10 2012

Status

approved