A266008 Number of n X 4 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.

1, 4, 4, 9, 14, 21, 44, 52, 129, 138, 361, 388, 980, 1129, 2614, 3325, 6924, 9764, 18369, 28370, 49105, 81348, 132708, 230281, 362782, 644837, 1001644, 1790932, 2785729, 4947162, 7781177, 13626564, 21772724, 37503337, 60913350, 103288269, 170189068

Offset

1,2

Links

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

Formula

Empirical: a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) - a(n-4).

Empirical g.f.: x*(1 + 2*x)*(1 + 3*x - x^2) / (1 + x - 3*x^2 - 3*x^3 + x^4). - Colin Barker, Jan 09 2019

Example

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

Crossrefs

Column 4 of A266012.

Sequence in context: A341678 A050218 A165996 * A284628 A262811 A294749

Adjacent sequences: A266005 A266006 A266007 * A266009 A266010 A266011

Keyword

nonn

Author

R. H. Hardin, Dec 20 2015

Status

approved