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A210406
Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.
1
7, 78, 864, 9576, 106128, 1176192, 13035456, 144468864, 1601114112, 17744767488, 196661044224, 2179547652096, 24155409051648, 267708662341632, 2966951532036096, 32882019268460544, 364423611069038592
OFFSET
1,1
COMMENTS
Column 1 of A210413.
LINKS
FORMULA
Empirical: a(n) = 10*a(n-1) + 12*a(n-2).
Conjectures from Colin Barker, Jul 15 2018: (Start)
G.f.: x*(7 + 8*x) / (1 - 10*x - 12*x^2).
a(n) = ((5-sqrt(37))^n*(-11+2*sqrt(37)) + (5+sqrt(37))^n*(11+2*sqrt(37))) / (6*sqrt(37)).
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..0....0..0....0..1....0..0....0..0....0..1....0..0....0..1....0..0
..1..2....1..2....1..2....0..2....1..2....1..2....0..2....1..2....2..3....1..2
..0..1....3..1....1..3....2..3....1..3....1..3....1..1....0..1....2..0....3..2
..1..2....1..2....1..2....0..2....2..1....3..2....3..0....1..2....1..1....0..1
..0..2....0..1....3..2....3..3....2..3....0..0....1..0....3..3....2..3....0..2
CROSSREFS
Cf. A210413.
Sequence in context: A210413 A045485 A068621 * A133272 A186657 A079590
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 21 2012
STATUS
approved