A197311 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

1, 0, 3, 2, 9, 6, 27, 18, 83, 56, 257, 176, 797, 556, 2475, 1766, 7699, 5640, 23995, 18106, 74937, 58408, 234541, 189266, 735771, 615834, 2313757, 2011340, 7294375, 6591454, 23056393, 21667064, 73073221, 71416640, 232226565, 235964308, 740061147

Offset

1,3

Comments

Every 0 is next to 0 0's, every 1 is next to 1 1'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 A197317.

Links

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

Formula

Empirical: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -9*a(n-4) +10*a(n-5) -3*a(n-7).

Empirical g.f.: x*(1 - x - 3*x^2 + 5*x^3 - 2*x^4 - 7*x^5 + 6*x^6) / ((1 - 3*x^2)*(1 - x - 3*x^2 + 3*x^3 - x^5)). - Colin Barker, May 12 2018

Example

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

Crossrefs

Cf. A197317.

Sequence in context: A349579 A082819 A298733 * A078478 A346109 A362220

Adjacent sequences: A197308 A197309 A197310 * A197312 A197313 A197314

Keyword

nonn

Author

R. H. Hardin, Oct 13 2011

Status

approved