A186564 Number of (n+2) X 7 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

12122, 2617, 4807, 11557, 21007, 23389, 27391, 33445, 44263, 68269, 104335, 154693, 256359, 394253, 582367, 921109, 1404439, 2088925, 3277999, 5032037, 7564615, 11783853, 18099679, 27341557, 42334903, 65029501, 98641359, 152194629

Offset

1,1

Comments

Column 5 of A186568.

Links

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

Formula

Empirical: a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)+2*a(n-6)-2*a(n-7) for n>13.

G.f.: x*(12122 - 21627*x + 11695*x^2 - 19684*x^3 + 45954*x^4 - 30458*x^5 - 31744*x^6 + 15662*x^7 + 14520*x^8 - 3552*x^9 - 10944*x^10 + 16928*x^12) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)) (conjectured). - Colin Barker, Jan 18 2018

Example

Some solutions for 4 X 7
..0..0..0..0..0..0..2....0..0..0..0..0..2..0....2..0..0..0..0..2..2
..0..0..0..0..0..0..2....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..0..0..0..0..0..2....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..1..0..0..0..0..2....1..2..0..0..0..0..2....0..2..0..0..0..0..0

Crossrefs

Sequence in context: A371952 A247403 A262635 * A247690 A126847 A018235

Adjacent sequences: A186561 A186562 A186563 * A186565 A186566 A186567

Keyword

nonn

Author

R. H. Hardin Feb 23 2011

Status

approved