A204278 Number of (n+2) X 4 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.

274, 622, 865, 193, 539, 735, 1883, 5187, 12715, 34507, 94379, 254955, 696107, 1902027, 5190667, 14180299, 38741771, 105832971, 289139339, 789944331, 2158145035, 5896158475, 16108606475, 44009485323, 120236143115, 328491255819

Offset

1,1

Comments

Column 2 of A204284.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-4) + 4*a(n-6) for n > 9.

Empirical g.f.: x*(274 - 200*x - 1001*x^2 - 2402*x^3 + 1604*x^4 + 2850*x^5 + 3772*x^6 - 1792*x^7 - 3072*x^8) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Jun 06 2018

Example

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

Crossrefs

Cf. A204284.

Sequence in context: A361797 A260289 A322254 * A165677 A143076 A171346

Adjacent sequences: A204275 A204276 A204277 * A204279 A204280 A204281

Keyword

nonn

Author

R. H. Hardin, Jan 13 2012

Status

approved