A210136 Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having one, two or four distinct values, and new values 0..3 introduced in row major order.

1, 10, 105, 1018, 9157, 77934, 638065, 5084818, 39762621, 306822358, 2345284009, 17806600698, 134548145461, 1013159874046, 7610346917985, 57063648570850, 427326717363757, 3197140079770278, 23904313586774425, 178642318573382986

Offset

1,2

Comments

Column 1 of A210143.

Links

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

Formula

Empirical: a(n) = 18*a(n-1) - 111*a(n-2) + 266*a(n-3) - 180*a(n-4) - 24*a(n-5) + 32*a(n-6).

Empirical g.f.: x*(1 - 8*x + 36*x^2 - 28*x^3 + 8*x^4) / ((1 - x)*(1 - 4*x)*(1 - 5*x - 2*x^2)*(1 - 8*x + 4*x^2)). - Colin Barker, Jul 14 2018

Example

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

Crossrefs

Cf. A210143.

Sequence in context: A268763 A300850 A360276 * A068093 A260214 A077369

Adjacent sequences: A210133 A210134 A210135 * A210137 A210138 A210139

Keyword

nonn

Author

R. H. Hardin, Mar 17 2012

Status

approved