A239531 Number of (n+1) X (2+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.

2, 2, 24, 68, 406, 1584, 7790, 33630, 156032, 695344, 3168922, 14262616, 64640674, 291830210, 1320357280, 5966652996, 26981170086, 121963213688, 551425857374, 2492844327694, 11270188295640, 50950869428672, 230346017497690

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 13*a(n-2) - a(n-3) - 23*a(n-4) - 28*a(n-5) + 11*a(n-6) + 40*a(n-7) - 9*a(n-8) - 5*a(n-9) + 5*a(n-10).

Empirical g.f.: 2*x*(1 - x - 3*x^2 - 2*x^3 + 3*x^4 + 7*x^5 - x^6 - x^7 + x^8) / (1 - 2*x - 13*x^2 + x^3 + 23*x^4 + 28*x^5 - 11*x^6 - 40*x^7 + 9*x^8 + 5*x^9 - 5*x^10). - Colin Barker, Oct 26 2018

Example

Some solutions for n=5:
..0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2....0..1..2
..0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2....0..1..2
..0..1..0....0..1..2....2..0..2....0..2..0....1..2..1....0..1..2....2..1..2
..2..1..0....0..1..2....2..0..2....0..2..0....1..2..1....0..1..2....2..1..2
..2..1..0....1..2..0....1..0..1....1..0..1....0..1..0....1..0..1....1..2..0
..2..1..0....1..2..0....1..0..1....1..0..1....0..1..0....1..0..1....1..2..0

Crossrefs

Column 2 of A239537.

Sequence in context: A272641 A334123 A127261 * A194130 A356908 A032336

Adjacent sequences: A239528 A239529 A239530 * A239532 A239533 A239534

Keyword

nonn

Author

R. H. Hardin, Mar 21 2014

Status

approved