A185837 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock trace equal to some horizontal or vertical neighbor 2 X 2 subblock trace.

0, 171, 405, 3249, 12609, 72225, 332937, 1731321, 8410473, 42400017, 209335185, 1045669905, 5189897529, 25851542121, 128510546841, 639547289793, 3180802829697, 15825291313473, 78719710355433, 391617249901785

Offset

1,2

Comments

Column 1 of A185845.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 15*a(n-3) + 120*a(n-4) - 144*a(n-5) + 144*a(n-6).

Empirical g.f.: 9*x^2*(19 - 69*x + 205*x^2 - 210*x^3 + 180*x^4) / (1 - 6*x + 6*x^2 + 15*x^3 - 120*x^4 + 144*x^5 - 144*x^6). - Colin Barker, Feb 28 2018

Example

Some solutions for 3 X 2:
..2..2....2..2....1..2....2..0....0..2....0..2....2..0....0..1....1..0....2..1
..2..0....2..0....1..2....2..2....0..1....1..1....0..0....2..2....1..1....1..0
..0..0....2..0....0..2....2..2....0..1....2..0....1..2....0..0....1..1....0..1

Crossrefs

Cf. A185845.

Sequence in context: A266315 A116459 A185610 * A016057 A043407 A031691

Adjacent sequences: A185834 A185835 A185836 * A185838 A185839 A185840

Keyword

nonn

Author

R. H. Hardin, Feb 05 2011

Status

approved