

A267905


Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in rowmajor sequential order.


1



1, 2, 5, 13, 34, 88, 225, 569, 1426, 3548, 8777, 21613, 53026, 129712, 316545, 770993, 1874914, 4553588, 11047625, 26779909, 64869586, 157043368, 380004897, 919150313, 2222499826, 5372538572, 12984354185, 31374801373, 75801065794
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OFFSET

1,2


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210


FORMULA

Empirical: a(n) = 5*a(n1) 7*a(n2) +a(n3) +2*a(n4).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(1  3*x + 2*x^2 + x^3) / ((1  x)*(1  2*x)*(1  2*x  x^2)).
a(n) = ((1sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)  2*(2^n1)) / 4.
(End)


EXAMPLE

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


CROSSREFS

Column 1 of A267911.
Sequence in context: A318234 A027931 A218481 * A209230 A103142 A112844
Adjacent sequences: A267902 A267903 A267904 * A267906 A267907 A267908


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 22 2016


STATUS

approved



