A205354 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.

14, 50, 194, 770, 3074, 12290, 49154, 196610, 786434, 3145730, 12582914, 50331650, 201326594, 805306370, 3221225474, 12884901890, 51539607554, 206158430210, 824633720834, 3298534883330, 13194139533314, 52776558133250

Offset

1,1

Comments

Column 1 of A205361.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 4*a(n-2).

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

G.f.: 2*x*(7 - 10*x) / ((1 - x)*(1 - 4*x)).

a(n) = 2 + 3*4^n.

(End)

Example

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

Crossrefs

Cf. A205361.

Sequence in context: A050441 A225921 A350850 * A281699 A082668 A231044

Adjacent sequences: A205351 A205352 A205353 * A205355 A205356 A205357

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved