A196596 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,4,0,3 for x=0,1,2,3,4.

1, 3, 16, 37, 116, 356, 1068, 3217, 9717, 29312, 88421, 266766, 804810, 2428010, 7325047, 22098889, 66669946, 201136011, 606805618, 1830666938, 5522924202, 16662065199, 50267649223, 151652062770, 457517876847, 1380281967900

Offset

1,2

Comments

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

Column 3 of A196601.

Links

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

Formula

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

Empirical g.f.: x*(1 + x + 8*x^2 - 4*x^3) / (1 - 2*x - 2*x^2 - 3*x^3 - x^4 + x^5). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196601.

Sequence in context: A173891 A066875 A294419 * A196573 A196804 A280093

Adjacent sequences: A196593 A196594 A196595 * A196597 A196598 A196599

Keyword

nonn

Author

R. H. Hardin, Oct 04 2011

Status

approved