A210127 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one, three or four distinct values, and new values 0..3 introduced in row major order.

8, 81, 897, 10019, 111993, 1251951, 13995437, 156453699, 1748981553, 19551704471, 218566712277, 2443337243979, 27313843108313, 305338948679391, 3413356121689917, 38157595235947859, 426560259838806273

Offset

1,1

Comments

Column 1 of A210134.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 9*a(n-2) - 2*a(n-3).

Empirical g.f.: x*(8 - 15*x - 3*x^2) / ((1 - x)*(1 - 11*x - 2*x^2)). - Colin Barker, Jul 14 2018

Example

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

Crossrefs

Cf. A210134.

Sequence in context: A324016 A068617 A207994 * A007778 A065440 A338694

Adjacent sequences: A210124 A210125 A210126 * A210128 A210129 A210130

Keyword

nonn

Author

R. H. Hardin, Mar 17 2012

Status

approved