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

1,1

Comments

Column 2 of A204076.

Links

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

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)

Example

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

Crossrefs

Cf. A204076.

Sequence in context: A007229 A367968 A297799 * A242209 A201244 A240263

Adjacent sequences: A204067 A204068 A204069 * A204071 A204072 A204073

Keyword

nonn

Author

R. H. Hardin, Jan 10 2012

Status

approved