A196859 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,4,2,0,1 for x=0,1,2,3,4.

1, 4, 12, 35, 102, 281, 787, 2237, 6346, 17976, 50903, 144132, 408157, 1155913, 3273609, 9270960, 26255482, 74355847, 210576950, 596357727, 1688896077, 4782984549, 13545499068, 38361099308, 108639331309, 307668565890

Offset

1,2

Comments

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

Column 4 of A196863.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -3*a(n-6) -6*a(n-7) -8*a(n-8) -8*a(n-9) -3*a(n-10).

Empirical g.f.: x*(1 + x + x^2 + x^3 + 2*x^4 - 11*x^5 - 13*x^6 - 6*x^7 - 5*x^8 - 3*x^9) / (1 - 3*x + x^2 - 2*x^3 + x^4 - x^5 + 3*x^6 + 6*x^7 + 8*x^8 + 8*x^9 + 3*x^10). - Colin Barker, May 09 2018

Example

Some solutions for n=5:
..0..2..2..0....0..2..2..2....0..0..0..0....0..0..0..0....2..2..0..0
..0..2..2..0....2..2..0..2....0..0..0..0....2..2..0..0....2..2..0..0
..0..0..0..0....2..0..0..2....0..0..0..0....2..2..0..0....0..1..0..0
..0..2..2..0....2..2..2..2....0..0..0..0....0..0..2..2....1..4..1..0
..0..2..2..0....0..0..0..0....0..0..0..0....0..0..2..2....0..1..0..0

Crossrefs

Cf. A196863.

Sequence in context: A318941 A079736 A035045 * A090328 A200541 A149318

Adjacent sequences: A196856 A196857 A196858 * A196860 A196861 A196862

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved