A205433 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..3 introduced in row major order.

15, 77, 443, 2705, 16955, 108173, 698747, 4558985, 29999531, 198898277, 1327629707, 8915678561, 60198810395, 408431259197, 2782950648923, 19033693298105, 130606895874635, 898770109853333, 6200177355415787

Offset

1,1

Comments

Column 1 of A205440.

Links

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

Formula

Empirical: a(n) = 21*a(n-1) - 156*a(n-2) + 442*a(n-3) - 81*a(n-4) - 1359*a(n-5) + 1134*a(n-6).

Empirical g.f.: x*(15 - 238*x + 1166*x^2 - 1216*x^3 - 3561*x^4 + 4914*x^5) / ((1 - x)*(1 - 3*x)*(1 - 6*x)*(1 - 7*x)*(1 - 4*x - 9*x^2)). - Colin Barker, Mar 03 2018

Example

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

Crossrefs

Cf. A205440.

Sequence in context: A051423 A205609 A257925 * A303097 A128272 A180579

Adjacent sequences: A205430 A205431 A205432 * A205434 A205435 A205436

Keyword

nonn

Author

R. H. Hardin, Jan 27 2012

Status

approved