A197539 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,2,1,1,1 for x=0,1,2,3,4.

1, 5, 8, 19, 28, 58, 119, 219, 395, 776, 1529, 2826, 5300, 10299, 19763, 37051, 70380, 135411, 257788, 487412, 929135, 1776855, 3377845, 6414026, 12229725, 23320560, 44346952, 84364697, 160777089, 306229857, 582642042, 1109154715, 2112783972

Offset

1,2

Comments

Every 0 is next to 0 2's, every 1 is next to 1 2'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 A197545.

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +4*a(n-4) -3*a(n-5) -a(n-6) +3*a(n-7) -2*a(n-8).

Empirical g.f.: x*(1 + 4*x + 3*x^2 + 9*x^3 - 5*x^4 - 3*x^5 + 7*x^6 - 6*x^7) / (1 - x - 2*x^3 - 4*x^4 + 3*x^5 + x^6 - 3*x^7 + 2*x^8). - Colin Barker, May 13 2018

Example

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

Crossrefs

Cf. A197545.

Sequence in context: A326826 A026595 A037233 * A034453 A269715 A271095

Adjacent sequences: A197536 A197537 A197538 * A197540 A197541 A197542

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved