A230825 Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.

0, 2, 2, 6, 16, 44, 124, 354, 1020, 2956, 8598, 25066, 73180, 213838, 625196, 1828502, 5348922, 15649258, 45788486, 133980160, 392046972, 1147212852, 3357028498, 9823567212, 28746526324, 84120672526, 246161907322, 720343138052

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-3) - a(n-4) for n>5.

Empirical g.f.: 2*x^2*(1 - x)*(1 - 2*x - x^2) / (1 - 4*x + 2*x^2 + 3*x^3 + x^4). - Colin Barker, Sep 22 2018

Example

All solutions for n=4:
..0..3....0..1....0..1....0..3....0..1....0..3
..1..2....3..2....3..2....1..2....3..2....1..2
..0..1....0..3....1..0....0..3....0..1....3..0
..3..2....1..2....2..3....1..2....3..2....2..1

Crossrefs

Column 2 of A230831.

Sequence in context: A067136 A180068 A034439 * A060165 A303150 A134295

Adjacent sequences: A230822 A230823 A230824 * A230826 A230827 A230828

Keyword

nonn

Author

R. H. Hardin, Oct 30 2013

Status

approved