A196212 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

3, 9, 20, 61, 189, 544, 1629, 4973, 15040, 45739, 140129, 429448, 1318027, 4054639, 12485046, 38469569, 118629261, 366006920, 1129623099, 3487480563, 10769378230, 33261326067, 102741225843, 317390237024, 980560274021, 3029559578685

Offset

1,1

Comments

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

Column 2 of A196218.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -8*a(n-4) -39*a(n-5) -33*a(n-6) -17*a(n-7) +5*a(n-8) +8*a(n-9) +a(n-10).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 4*x^4 + 15*x^5 + 3*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - 2*x^4 + x^5 + x^6)). - Colin Barker, Feb 22 2018

Example

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

Crossrefs

Cf. A196218.

Sequence in context: A146267 A151420 A196294 * A146219 A197403 A305618

Adjacent sequences: A196209 A196210 A196211 * A196213 A196214 A196215

Keyword

nonn

Author

R. H. Hardin, Sep 29 2011

Status

approved