A197497 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,1,1,0 for x=0,1,2,3,4.

1, 1, 9, 9, 19, 45, 73, 147, 291, 539, 1051, 2025, 3863, 7451, 14313, 27465, 52817, 101457, 194891, 374517, 719505, 1382347, 2655995, 5102835, 9804019, 18836497, 36190191, 69531891, 133591057, 256666833, 493131481, 947448537, 1820322627

Offset

1,3

Comments

Every 0 is next to 0 2'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 0's.

Column 2 of A197503.

Links

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

Formula

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

Empirical g.f.: x*(1 + 7*x^2 - 3*x^3) / (1 - x - x^2 - 2*x^3 + x^4). - Colin Barker, May 12 2018

Example

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

Crossrefs

Cf. A197503.

Sequence in context: A245430 A161365 A214831 * A053456 A144424 A359038

Adjacent sequences: A197494 A197495 A197496 * A197498 A197499 A197500

Keyword

nonn

Author

R. H. Hardin, Oct 15 2011

Status

approved