A230929 Number of black-square subarrays of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

2, 6, 16, 48, 146, 438, 1312, 3936, 11810, 35430, 106288, 318864, 956594, 2869782, 8609344, 25828032, 77484098, 232452294, 697356880, 2092070640, 6276211922, 18828635766, 56485907296, 169457721888, 508373165666, 1525119496998

Offset

1,1

Comments

Column 2 of A230935.

Links

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

Formula

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

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

Example

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

Crossrefs

Cf. A230935.

Sequence in context: A129772 A360856 A046721 * A367042 A291189 A214843

Adjacent sequences: A230926 A230927 A230928 * A230930 A230931 A230932

Keyword

nonn

Author

R. H. Hardin, Nov 01 2013

Status

approved