A196918 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,4,0 for x=0,1,2,3,4.

1, 4, 12, 37, 114, 335, 1003, 3051, 9290, 28268, 86013, 261786, 796995, 2426793, 7389825, 22503304, 68527674, 208684983, 635506294, 1935309489, 5893618625, 17947924171, 54657124744, 166448373086, 506888519813, 1543637889196

Offset

1,2

Comments

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

Column 4 of A196922.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) -a(n-4) -a(n-5) -5*a(n-6) -8*a(n-7) -3*a(n-8) for n>9.

Empirical g.f.: x*(1 - x^2 - x^4 - 17*x^5 - 11*x^6 + 7*x^7 + 6*x^8) / (1 - 4*x + 3*x^2 - x^3 + x^4 + x^5 + 5*x^6 + 8*x^7 + 3*x^8). - Colin Barker, May 10 2018

Example

Some solutions for n=5:
..0..0..0..0....0..2..2..0....0..0..0..0....0..2..2..2....0..0..0..0
..0..0..0..0....0..2..2..0....0..0..2..2....0..2..0..2....0..4..0..0
..2..2..0..0....0..0..0..0....0..0..2..2....0..2..0..2....0..0..2..2
..2..2..0..0....2..2..0..0....0..0..0..0....0..2..2..2....0..0..2..2
..0..0..0..0....2..2..0..0....0..0..0..0....0..0..0..0....0..0..0..0

Crossrefs

Cf. A196922.

Sequence in context: A279277 A101555 A033130 * A099098 A019481 A019480

Adjacent sequences: A196915 A196916 A196917 * A196919 A196920 A196921

Keyword

nonn

Author

R. H. Hardin, Oct 07 2011

Status

approved