A210313 Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having two or three distinct values, and new values 0..3 introduced in row major order.

0, 35, 995, 19186, 319485, 4963700, 74362241, 1091691712, 15840736305, 228277891400, 3276198192905, 46903413280504, 670487434284753, 9575993410570520, 136690481022953081, 1950506854209691864

Offset

1,2

Comments

Column 1 of A210320.

Links

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

Formula

Empirical: a(n) = 24*a(n-1) - 141*a(n-2) - 24*a(n-3) + 718*a(n-4) + 768*a(n-5) + 216*a(n-6).

Empirical g.f.: x^2*(35 + 155*x + 241*x^2 + 156*x^3 + 36*x^4) / ((1 - 3*x - 2*x^2)*(1 - 8*x - 6*x^2)*(1 - 13*x - 18*x^2)). - Colin Barker, Jul 15 2018

Example

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

Crossrefs

Cf. A210320.

Sequence in context: A115473 A002453 A240826 * A049395 A278723 A215296

Adjacent sequences: A210310 A210311 A210312 * A210314 A210315 A210316

Keyword

nonn

Author

R. H. Hardin, Mar 20 2012

Status

approved