A204638 Number of (n+2) X 6 0..3 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..3 introduced in row major order.

4246, 379, 933, 478, 1169, 4366, 8179, 29877, 113861, 407328, 1541643, 5847274, 22096265, 83765839, 317588101, 1203850602, 4564121261, 17303919222, 65603484087, 248721618481, 942975306533, 3575088842524, 13554190638871

Offset

1,1

Comments

Column 4 of A204642.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10.

Empirical g.f.: x*(4246 - 20851*x + 11776*x^2 + 13934*x^3 + 54046*x^4 - 42717*x^5 - 90750*x^6 + 31551*x^7 + 36801*x^8 + 504*x^9) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - 3*x^2)*(1 - 3*x^3)). - Colin Barker, Jun 08 2018

Example

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

Crossrefs

Cf. A204642.

Sequence in context: A254880 A184684 A204872 * A205995 A237805 A031985

Adjacent sequences: A204635 A204636 A204637 * A204639 A204640 A204641

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved