

A267946


Number of n X 1 0..2 arrays with every repeated value in every row and column one larger mod 3 than the previous repeated value, and upper left element zero.


2



1, 3, 8, 21, 53, 132, 323, 783, 1880, 4485, 10637, 25116, 59075, 138519, 323936, 755877, 1760453, 4093620, 9506051, 22049055, 51091496, 118287237, 273658877, 632714892, 1462080131, 3377002023, 7796796848, 17994911781, 41519520053
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OFFSET

1,2


COMMENTS



LINKS



FORMULA

Empirical: a(n) = 3*a(n1) + a(n2)  6*a(n3).
G.f.: x*(1  2*x^2) / ((1  2*x)*(1  x  3*x^2)).
a(n) = 2^(n)*(39*4^n + (267*sqrt(13))*(1sqrt(13))^n + (1+sqrt(13))^n*(26+7*sqrt(13))) / 39.
(End)


EXAMPLE

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..2....1....1....2....0....2....1....1....1....2....0....2....2....0....1....2
..1....2....0....0....2....1....0....2....2....1....2....2....0....2....2....0
..1....0....1....2....0....0....1....0....0....0....0....0....2....1....2....2
..0....1....1....1....2....2....0....1....2....1....2....0....0....2....0....0
..1....1....0....2....1....0....0....0....0....2....1....1....2....1....0....1
..0....2....2....1....2....2....2....0....1....1....0....2....2....1....1....2
..2....2....1....0....1....1....1....2....0....0....1....0....0....0....0....2


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



