A230928 Number of black-square subarrays of (n+2) X (1+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, 2, 8, 8, 42, 42, 208, 208, 1042, 1042, 5208, 5208, 26042, 26042, 130208, 130208, 651042, 651042, 3255208, 3255208, 16276042, 16276042, 81380208, 81380208, 406901042, 406901042, 2034505208, 2034505208, 10172526042, 10172526042

Offset

1,1

Comments

Column 1 of A230935.

Links

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

Formula

Empirical: a(n) = 4*a(n-2) + 5*a(n-4).

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

Example

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

Crossrefs

Cf. A230935.

Sequence in context: A281019 A325513 A144060 * A016119 A037223 A066988

Adjacent sequences: A230925 A230926 A230927 * A230929 A230930 A230931

Keyword

nonn

Author

R. H. Hardin, Nov 01 2013

Status

approved