A206163 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.

85, 1070, 17142, 238182, 3814022, 53494742, 850283062, 12012206406, 189640648294, 2696243766070, 42310772017430, 604975719064998, 9442901799738950, 135699248890772630, 2108048210361864694

Offset

1,1

Comments

Column 2 of A206169.

Links

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

Formula

Empirical: a(n) = a(n-1) + 217*a(n-2) - 33*a(n-3) - 1320*a(n-4) - 432*a(n-5) + 1152*a(n-6) for n>7.

Empirical g.f.: x*(85 + 985*x - 2373*x^2 - 8345*x^3 + 3536*x^4 + 10032*x^5 - 2688*x^6) / ((1 - x - 4*x^2)*(1 - 213*x^2 - 180*x^3 + 288*x^4)). - Colin Barker, Jun 13 2018

Example

Some solutions for n=4:
..0..1..0....0..0..0....0..0..0....0..1..0....0..1..0....0..0..1....0..1..0
..0..0..2....0..1..0....0..0..0....1..0..1....1..0..1....1..0..0....0..0..0
..3..3..1....3..1..0....2..3..2....0..2..0....3..1..3....1..2..3....1..1..1
..1..3..3....0..3..1....3..1..3....1..3..3....2..2..2....2..2..2....0..1..3
..0..2..0....2..3..2....1..3..1....3..0..3....1..2..3....1..1..0....2..1..2

Crossrefs

Cf. A206169.

Sequence in context: A194533 A069308 A183643 * A020239 A297587 A189439

Adjacent sequences: A206160 A206161 A206162 * A206164 A206165 A206166

Keyword

nonn

Author

R. H. Hardin, Feb 04 2012

Status

approved