A197344 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,1,1,0 for x=0,1,2,3,4.

1, 1, 9, 17, 33, 89, 249, 553, 1321, 3361, 8281, 19801, 48561, 119729, 292017, 711473, 1743129, 4266529, 10420753, 25472041, 62314921, 152363161, 372445401, 910689521, 2226903849, 5444657417, 13311984513, 32549302369, 79585485409

Offset

1,3

Comments

Every 0 is next to 0 3'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 A197350.

Links

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

Formula

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

Empirical g.f.: x*(1 + 7*x^2 + 3*x^3 - 4*x^4) / (1 - x - x^2 - 4*x^3 - 7*x^4 + 4*x^5). - Colin Barker, Feb 22 2018

Example

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

Crossrefs

Cf. A197350.

Sequence in context: A111733 A127193 A262453 * A146236 A147279 A173788

Adjacent sequences: A197341 A197342 A197343 * A197345 A197346 A197347

Keyword

nonn

Author

R. H. Hardin, Oct 13 2011

Status

approved