A233099 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

3, 11, 65, 386, 2315, 13886, 83315, 499886, 2999315, 17995886, 107975315, 647851886, 3887111315, 23322667886, 139936007315, 839616043886, 5037696263315, 30226177579886, 181357065479315, 1088142392875886

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + a(n-2) - 6*a(n-3) for n>4.

Conjectures from Colin Barker, Oct 07 2018: (Start)

G.f.: x*(3 - 7*x - 4*x^2 + 3*x^3) / ((1 - x)*(1 + x)*(1 - 6*x)).

a(n) = (24 + 25*6^n) / 84 for n even.

a(n) = (60 + 25*6^n) / 84 for n>1 and odd.

(End)

Example

Some solutions for n=5:
..0..1..0..1..3....0..1..3..2..0....0..0..0..0..1....0..1..1..1..0
..0..0..1..1..3....0..2..0..1..0....1..0..1..0..1....0..0..1..0..1

Crossrefs

Row 2 of A233098.

Sequence in context: A096655 A030226 A309174 * A372395 A132101 A280775

Adjacent sequences: A233096 A233097 A233098 * A233100 A233101 A233102

Keyword

nonn

Author

R. H. Hardin, Dec 04 2013

Status

approved