A196316 - OEIS

A196316

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

1, 7, 10, 23, 57, 122, 275, 623, 1394, 3133, 7045, 15824, 35557, 79901, 179530, 403401, 906439, 2036744, 4576523, 10283359, 23106492, 51919817, 116662775, 262138870, 589020695, 1323517493, 2973916806, 6682330407, 15015060135, 33738533866

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

Column 2 of A196322.

LINKS

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

FORMULA

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

Empirical g.f.: x*(1 + 6*x + x^2 - 3*x^3) / ((1 + x + x^2)*(1 - 2*x - x^2 + x^3)). - Colin Barker, Feb 18 2018

EXAMPLE

Some solutions for n=4:

..0..0....2..0....0..2....0..0....0..2....0..0....0..0....0..2....0..0....0..2

..0..2....0..2....2..0....0..0....0..0....0..0....0..2....0..0....2..2....0..0

..0..2....0..2....2..0....0..0....0..0....0..0....0..2....0..0....0..0....0..0

..2..0....0..0....0..2....0..2....0..2....2..0....0..0....0..0....2..0....2..0

CROSSREFS

Sequence in context: A103119 A054224 A183330 * A134329 A175492 A241052

Adjacent sequences: A196313 A196314 A196315 * A196317 A196318 A196319

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 01 2011

STATUS

approved