A240637 Number of n X 2 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

1, 5, 27, 193, 1391, 10072, 72941, 528283, 3826157, 27711478, 200704271, 1453628917, 10528111931, 76251331828, 552260998337, 3999827976463, 28969316843801, 209814352850962, 1519609968699971, 11005988987858473

Offset

1,2

Comments

Column 2 of A240642.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 10*a(n-2) - 6*a(n-3) - 9*a(n-4) for n>6.

Empirical g.f.: x*(1 - x - 13*x^2 - 13*x^3 + 2*x^4 + 3*x^5) / ((1 - x)*(1 + x)*(1 - 6*x - 9*x^2)). - Colin Barker, Mar 19 2018

Example

Some solutions for n=4:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....1..2....2..0....1..0....2..3....1..0....2..0....2..0....2..3....1..2
..2..1....3..1....0..2....2..1....0..2....2..2....3..2....0..2....0..1....2..1
..3..0....2..3....3..1....0..2....3..0....2..2....0..1....1..0....1..3....0..2

Crossrefs

Cf. A240642.

Sequence in context: A367048 A326094 A232683 * A023811 A126119 A105631

Adjacent sequences: A240634 A240635 A240636 * A240638 A240639 A240640

Keyword

nonn

Author

R. H. Hardin, Apr 09 2014

Status

approved