A230701 Number of (n+3) X (1+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

2, 8, 30, 102, 348, 1172, 3956, 13326, 44916, 151338, 509978, 1718408, 5790456, 19511640, 65747178, 221543696, 746521190, 2515502046, 8476319172, 28562083692, 96243740012, 324306077270, 1092792451740, 3682309466130, 12408031373682

Offset

1,1

Comments

Column 1 of A230708.

Links

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

Formula

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

Empirical g.f.: 2*x*(1 + x) / ((1 - x)*(1 - 2*x - 5*x^2 + x^3 + x^4)). - Colin Barker, Mar 17 2018

Example

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

Crossrefs

Cf. A230708.

Sequence in context: A010749 A299415 A364078 * A365693 A168605 A127865

Adjacent sequences: A230698 A230699 A230700 * A230702 A230703 A230704

Keyword

nonn

Author

R. H. Hardin, Oct 28 2013

Status

approved