A204070 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

38, 329, 2882, 25277, 221726, 1944977, 17061338, 149662085, 1312836086, 11516200601, 101020133234, 886148797901, 7773298914638, 68187392635937, 598139935894154, 5246884637775509, 46025681868191270, 403737367538170409

Offset: 1

Author

R. H. Hardin, Jan 10 2012

Keywords

• nonn

Comments

Column 2 of A204076.

Examples

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

Links

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

Crossrefs

Cf. A204076.

Formula

Empirical: a(n) = 10*a(n-1) - 11*a(n-2) + 2*a(n-3).

Conjectures from Colin Barker, Jun 06 2018: (Start)

G.f.: x*(38 - 51*x + 10*x^2) / ((1 - x)*(1 - 9*x + 2*x^2)).

a(n) = 1/2 + (2^(-2-n)*(3*(9+sqrt(73))^n*(23+3*sqrt(73)) + (9-sqrt(73))^n*(-69+9*sqrt(73)))) / sqrt(73).

(End)