A280393 Number of n X 3 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 6, 66, 554, 4250, 31242, 223706, 1571978, 10887706, 74545802, 505624538, 3402833418, 22750442266, 151248129802, 1000625900506, 6591782458762, 43261686405658, 282980475181450, 1845507292321242, 12003609559311114

Offset

1,1

Links

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

Formula

Empirical: a(n) = 18*a(n-1) - 121*a(n-2) + 392*a(n-3) - 688*a(n-4) + 640*a(n-5) - 256*a(n-6) for n>7.

Empirical g.f.: 2*x*(1 - 2*x)*(1 - 13*x + 74*x^2 - 198*x^3 + 248*x^4 - 128*x^5) / (1 - 9*x + 20*x^2 - 16*x^3)^2. - Colin Barker, Feb 13 2019

Example

Some solutions for n=4:
..0..0..1. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
..0..1..1. .1..2..2. .1..1..1. .0..1..2. .1..1..1. .1..1..1. .1..1..1
..0..0..1. .2..0..0. .0..1..1. .2..2..2. .2..1..1. .2..2..2. .1..1..0
..0..0..0. .0..0..0. .1..1..1. .2..2..2. .1..1..1. .1..2..2. .1..1..1

Crossrefs

Column 3 of A280398.

Sequence in context: A368511 A368512 A262047 * A239696 A335645 A082619

Adjacent sequences: A280390 A280391 A280392 * A280394 A280395 A280396

Keyword

nonn

Author

R. H. Hardin, Jan 02 2017

Status

approved