A204639 Number of (n+2) X 7 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.

16855, 1860, 760, 1169, 3300, 3077, 9482, 35500, 109224, 410467, 1557742, 5832593, 22104912, 83813366, 317543288, 1203875773, 4564263072, 17303784013, 65603558830, 248722043144, 942974900136, 3575089065983, 13554191912090

Offset

1,1

Comments

Column 5 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*(16855 - 82415*x + 42025*x^2 + 70369*x^3 + 209435*x^4 - 186816*x^5 - 358482*x^6 + 128064*x^7 + 150525*x^8 + 5130*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..0..1..0..1..2..0....0..1..2..2..2..0..0
..0..0..0..0..0..0..0....0..0..1..0..1..2..0....0..2..2..2..0..0..0
..1..1..1..1..1..1..1....0..0..1..0..1..2..0....2..2..2..0..0..0..3
..2..2..2..2..2..2..2....0..0..1..0..1..2..0....2..2..0..0..0..3..3
..1..1..1..1..1..1..1....0..0..1..0..1..2..0....2..0..0..0..3..3..3

Crossrefs

Cf. A204642.

Sequence in context: A203891 A088164 A234699 * A233986 A170797 A259426

Adjacent sequences: A204636 A204637 A204638 * A204640 A204641 A204642

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved