A205163 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..3 introduced in row major order.

13, 159, 2277, 33831, 506493, 7594479, 113908437, 1708600311, 25628925933, 384433652799, 5766504083397, 86497559125191, 1297463380500573, 19461950688376719, 291929260268255157, 4378938903851640471

Offset: 1

Author

R. H. Hardin, Jan 22 2012

Keywords

• nonn

Comments

Column 1 of A205170.

Examples

			Some solutions for n=4:
  0 1   0 1   0 0   0 0   0 0   0 0   0 0   0 0   0 0   0 1
  0 1   1 1   1 0   0 1   0 1   0 1   0 1   0 1   0 1   0 1
  0 0   0 0   0 2   0 2   1 2   0 2   2 0   1 2   2 0   0 0
  0 1   0 1   1 3   1 3   1 3   2 1   3 1   0 1   0 1   1 0
  1 1   0 0   0 1   2 0   0 0   1 0   1 2   0 0   3 0   2 3
		

Links

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

Crossrefs

Cf. A205170.

Formula

Empirical: a(n) = 18*a(n-1) - 45*a(n-2).

Conjectures from Colin Barker, Mar 03 2018: (Start)

G.f.: x*(13 - 75*x) / ((1 - 3*x)*(1 - 15*x)).

a(n) = 3^(n-1)*(2*5^n+3).

(End)