A210101 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.

30, 225, 1690, 12725, 95830, 721705, 5435250, 40933565, 308275950, 2321665905, 17484765130, 131680019525, 991699197190, 7468614458425, 56247097997730, 423604143817805, 3190217398715550, 24025938366280065, 180942438158822650

Offset

1,1

Comments

Column 2 of A210107.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 3*a(n-2) - 4*a(n-3).

Conjectures from Colin Barker, Jul 14 2018: (Start)

G.f.: 5*x*(6 - 3*x - 4*x^2) / ((1 - x)*(1 - 7*x - 4*x^2)).

a(n) = (1/13)*2^(-2-n)*(13*2^(1+n) + (117-11*sqrt(65))*(7-sqrt(65))^n + (7+sqrt(65))^n*(117+11*sqrt(65))).

(End)

Example

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

Crossrefs

Cf. A210107.

Sequence in context: A076389 A342896 A189410 * A156372 A064241 A080569

Adjacent sequences: A210098 A210099 A210100 * A210102 A210103 A210104

Keyword

nonn

Author

R. H. Hardin, Mar 17 2012

Status

approved