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A198287
Number of 2n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor.
2
2, 17, 272, 4667, 80702, 1397477, 24207692, 419373647, 7265397242, 125869473977, 2180631250952, 37778460128867, 654494991508022, 11338834542738317, 196440265628093252, 3403240245856247927, 58959623892961901042
OFFSET
1,1
COMMENTS
Column 1 of A198290.
LINKS
FORMULA
Empirical: a(n) = 23*a(n-1) - 103*a(n-2) + 81*a(n-3).
Conjectures from Colin Barker, Mar 02 2018: (Start)
G.f.: x*(2 - 29*x + 87*x^2) / ((1 - x)*(1 - 22*x + 81*x^2)).
a(n) = (216 - (11-2*sqrt(10))^n*(-8+sqrt(10)) + (8+sqrt(10))*(11+2*sqrt(10))^n) / 216.
(End)
EXAMPLE
Some solutions for n=2:
..0..1....0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0....0..0
..0..1....1..2....1..1....1..1....1..1....1..1....1..1....0..1....1..1....1..2
..2..2....1..2....2..2....0..0....0..2....2..0....2..2....2..2....0..0....1..2
..0..0....3..3....1..1....2..2....0..2....2..0....0..0....1..1....1..1....0..0
CROSSREFS
Cf. A198290.
Sequence in context: A195443 A176585 A086534 * A338635 A268705 A078367
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 23 2011
STATUS
approved