A230930 Number of black-square subarrays of (n+2) X (3+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.

8, 16, 102, 232, 1682, 3768, 27106, 60824, 437930, 982552, 7073698, 15870936, 114260634, 256361112, 1845635570, 4140964568, 29812290666, 66888415128, 481553712898, 1080439106264, 7778468998714, 17452180031640, 125644509294994

Offset

1,1

Links

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

Formula

Empirical: a(n) = 16*a(n-2) + 3*a(n-4) - 10*a(n-6) + 24*a(n-8) - 16*a(n-10).

Empirical g.f.: 2*x*(4 + 8*x - 13*x^2 - 12*x^3 + 13*x^4 + 4*x^5 - 16*x^6 + 8*x^8) / (1 - 16*x^2 - 3*x^4 + 10*x^6 - 24*x^8 + 16*x^10). - Colin Barker, Sep 23 2018

Example

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

Crossrefs

Column 3 of A230935.

Sequence in context: A291001 A062508 A083086 * A080452 A270377 A264472

Adjacent sequences: A230927 A230928 A230929 * A230931 A230932 A230933

Keyword

nonn

Author

R. H. Hardin, Nov 01 2013

Status

approved