A197617 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,1,1,1 for x=0,1,2,3,4.

0, 0, 8, 0, 8, 32, 16, 64, 152, 160, 424, 832, 1216, 2688, 4968, 8384, 16936, 30944, 55440, 107072, 196152, 359776, 679880, 1251456, 2315136, 4330752, 8000840, 14842752, 27638984, 51176864, 95010832, 176575552, 327357272, 607795744

Offset

1,3

Comments

Every 0 is next to 0 0's, every 1 is next to 1 3's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.

Column 2 of A197623.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

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

Empirical g.f.: 8*x^3 / (1 - x^2 - 4*x^3 - x^4). - Colin Barker, May 14 2018

Example

All solutions for n=5:
..0..1....1..0....1..2....1..0....1..2....2..1....2..1....0..1
..1..3....3..1....3..1....3..1....3..1....1..3....1..3....1..3
..1..1....1..1....1..1....1..1....1..1....1..1....1..1....1..1
..3..1....1..3....1..3....1..3....1..3....3..1....3..1....3..1
..1..0....0..1....0..1....2..1....2..1....1..0....1..2....1..2

Crossrefs

Cf. A197623.

Sequence in context: A055959 A341485 A076350 * A005076 A296182 A019863

Adjacent sequences: A197614 A197615 A197616 * A197618 A197619 A197620

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved