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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 10 2012
STATUS
approved