A196317 Number of n X 3 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.

2, 10, 30, 88, 299, 978, 3132, 10106, 32721, 105779, 341872, 1105228, 3573075, 11550674, 37340085, 120711068, 390227727, 1261503955, 4078113677, 13183480921, 42618760767, 137775353596, 445391843834, 1439835858140, 4654614404396

Offset

1,1

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 3 of A196322.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 2*a(n-3) + 4*a(n-4) - 2*a(n-5) + 3*a(n-6) + 7*a(n-7) - a(n-8) - 10*a(n-9) - 9*a(n-10) - 2*a(n-11).

Empirical g.f.: x*(2 + 6*x + 4*x^2 - 6*x^3 + 5*x^4 + 20*x^5 - 3*x^6 - 26*x^7 - 21*x^8 - 3*x^9 + 2*x^10) / (1 - 2*x - 3*x^2 - 2*x^3 - 4*x^4 + 2*x^5 - 3*x^6 - 7*x^7 + x^8 + 10*x^9 + 9*x^10 + 2*x^11). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A196322.

Sequence in context: A058967 A355775 A234471 * A318579 A064932 A343513

Adjacent sequences: A196314 A196315 A196316 * A196318 A196319 A196320

Keyword

nonn

Author

R. H. Hardin, Oct 01 2011

Status

approved