A253029 - OEIS

A253029

Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.

297, 1647, 9126, 50571, 280233, 1552878, 8605089, 47684079, 264235662, 1464230547, 8113859721, 44961990246, 249151530393, 1380643622703, 7650672704694, 42395294391579, 234928490071977, 1301828333534622

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 5*a(n-1) + 3*a(n-2).

Conjectures from Colin Barker, Dec 08 2018: (Start)

G.f.: 27*x*(11 + 6*x) / (1 - 5*x - 3*x^2).

a(n) = (27*2^(-n)*((5-sqrt(37))^n*(-6+sqrt(37)) + (5+sqrt(37))^n*(6+sqrt(37)))) / sqrt(37).

(End)

EXAMPLE

Some solutions for n=4:

..0..1..0....0..1..0....0..0..1....0..0..1....0..1..1....0..0..1....0..0..1

..0..2..0....1..0..0....1..0..0....1..1..2....2..1..1....2..1..2....1..2..2

..2..1..2....0..0..1....0..1..1....0..0..2....0..0..2....0..0..1....0..0..1

..0..2..2....0..1..0....0..1..0....1..1..0....0..0..2....0..0..2....1..2..1

..0..1..1....1..0..1....1..0..1....0..0..2....2..2..1....2..1..1....0..2..0

..2..1..2....1..0..0....0..1..1....0..0..2....2..0..2....2..0..2....0..0..1

CROSSREFS

Column 1 of A253035.

Sequence in context: A179158 A037043 A253035 * A251289 A281132 A200855

Adjacent sequences: A253026 A253027 A253028 * A253030 A253031 A253032

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 26 2014

STATUS

approved