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A278008
Number of n X 2 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
1
0, 6, 30, 198, 1230, 7734, 48510, 304422, 1910190, 11986326, 75213150, 471956358, 2961486990, 18583085814, 116607324990, 731701311462, 4591365157230, 28810436277846, 180783102647070, 1134399003458118, 7118259838467150
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) + 8*a(n-2).
Conjectures from Colin Barker, Feb 07 2019: (Start)
G.f.: 6*x^2 / (1 - 5*x - 8*x^2).
a(n) = 2^(-3-n) * ((57-5*sqrt(57))*(5+sqrt(57))^n + (5-sqrt(57))^n*(57+5*sqrt(57))) / 19.
(End)
EXAMPLE
Some solutions for n=4:
..0..1. .0..2. .0..1. .0..1. .0..1. .0..1. .0..1. .0..2. .0..2. .0..2
..0..2. .1..2. .0..2. .0..2. .0..2. .2..2. .1..2. .1..1. .1..1. .1..0
..2..1. .2..0. .2..0. .1..2. .1..2. .1..1. .0..1. .0..1. .0..2. .2..1
..2..0. .2..1. .1..1. .0..0. .1..1. .0..2. .0..0. .2..2. .1..1. .0..1
CROSSREFS
Column 2 of A278014.
Sequence in context: A147517 A294221 A005922 * A370751 A325950 A275953
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 08 2016
STATUS
approved