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

1,1

Comments

Column 1 of A205170.

Links

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

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)

Example

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

Crossrefs

Cf. A205170.

Sequence in context: A084328 A000830 A205170 * A118673 A216300 A250417

Adjacent sequences: A205160 A205161 A205162 * A205164 A205165 A205166

Keyword

nonn

Author

R. H. Hardin, Jan 22 2012

Status

approved