A204641 Number of (n+2) X 9 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.

144255, 8140, 9750, 8179, 9482, 16171, 16636, 40170, 134630, 418053, 1557876, 5894935, 22113794, 83799892, 317716438, 1203888543, 4564208774, 17304289587, 65603583264, 248721866374, 942976402982, 3575089125409, 13554191367904

Offset

1,1

Comments

Column 7 of A204642.

Links

R. H. Hardin, Table of n, a(n) for n = 1..121

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*(144255 - 713135*x + 401815*x^2 + 560869*x^3 + 1761457*x^4 - 1601082*x^5 - 3013092*x^6 + 1151934*x^7 + 1230813*x^8 + 1476*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..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1
..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1
..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1
..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1
..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

Crossrefs

Cf. A204642.

Sequence in context: A004042 A145742 A236995 * A133324 A348808 A209968

Adjacent sequences: A204638 A204639 A204640 * A204642 A204643 A204644

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved