A197531 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

3, 9, 16, 33, 73, 160, 361, 835, 1966, 4703, 11399, 27914, 68903, 171121, 426940, 1068865, 2682789, 6746336, 16988333, 42822747, 108024178, 272648551, 688426371, 1738750602, 4392467427, 11098043841, 28043540864, 70868720569, 179102669081

Offset

1,1

Comments

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

Column 2 of A197537.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-3) - 4*a(n-4) - 3*a(n-5) + a(n-7) + a(n-8).

Empirical g.f.: x*(1 + x)^2*(3 - 6*x - 2*x^2 - 2*x^3 + x^4 + 2*x^5) / ((1 - x - x^2 - x^3)*(1 - 2*x - x^2 - x^3 + x^5)). - Colin Barker, Mar 02 2018

Example

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

Crossrefs

Cf. A197537.

Sequence in context: A257034 A232167 A058538 * A117108 A223188 A145796

Adjacent sequences: A197528 A197529 A197530 * A197532 A197533 A197534

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved