A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

1, 7, 48, 321, 2175, 14748, 99933, 677283, 4590168, 31108893, 210834267, 1428886932, 9683993481, 65631317487, 444803049600, 3014563174089, 20430595384935, 138464249604684, 938413592805957, 6359909317239723

Offset

1,2

Comments

Column 2 of A186168.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 11*a(n-2) + 9*a(n-3) - 9*a(n-4) - 27*a(n-5).

Empirical g.f.: x*(1 + 2*x + 2*x^2 - 5*x^3 - 12*x^4) / (1 - 5*x - 11*x^2 - 9*x^3 + 9*x^4 + 27*x^5). - Colin Barker, Apr 17 2018

Example

Some solutions for 4 X 2 with a(1,1)=0:
..0..0....0..1....0..0....0..0....0..3....0..2....0..0....0..2....0..2....0..0
..2..2....0..1....2..3....1..1....0..3....0..2....0..2....0..2....0..2....0..0
..0..2....3..3....2..3....3..3....2..0....0..2....3..2....3..3....1..1....2..2
..0..0....0..0....1..1....3..3....2..0....0..2....3..3....3..3....1..1....0..0

Crossrefs

Cf. A186168.

Sequence in context: A227100 A240334 A171312 * A370037 A081106 A289785

Adjacent sequences: A186158 A186159 A186160 * A186162 A186163 A186164

Keyword

nonn

Author

R. H. Hardin, Feb 13 2011

Status

approved