A253020 Number of (n+2) X (3+2) 0..3 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.

51, 83, 133, 120, 219, 350, 302, 531, 846, 754, 1323, 2100, 1888, 3287, 5198, 4734, 8185, 12894, 11890, 20411, 32028, 29912, 50981, 79678, 75374, 127541, 198526, 190242, 319593, 495428, 480944, 802149, 1238334, 1217806, 2016627, 3100254

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-3) - 6*a(n-6) - a(n-9) + a(n-12) for n>15.

Empirical g.f.: x*(51 + 83*x + 133*x^2 - 135*x^3 - 196*x^4 - 315*x^5 + 8*x^6 - 66*x^7 - 106*x^8 + 15*x^9 + 65*x^10 + 103*x^11 - x^12 - 6*x^13 - 9*x^14) / ((1 - 3*x^3 + x^6)*(1 - 2*x^3 - x^6)). - Colin Barker, Dec 08 2018

Example

Some solutions for n=4:
..0..1..2..0..1....0..0..0..0..0....0..0..0..0..0....0..1..2..0..3
..1..0..2..1..0....1..2..0..1..2....1..2..0..1..2....2..2..2..2..2
..2..2..2..2..2....2..1..0..2..1....2..1..0..2..1....3..0..2..1..0
..0..1..2..0..3....0..0..0..0..0....0..0..0..0..0....0..3..2..0..1
..1..0..2..3..0....1..2..0..1..3....3..2..0..1..3....2..2..2..2..2
..2..2..2..2..2....2..3..0..2..1....2..1..0..2..1....3..0..2..3..0

Crossrefs

Column 3 of A253025.

Sequence in context: A113285 A050698 A039474 * A351026 A020180 A049328

Adjacent sequences: A253017 A253018 A253019 * A253021 A253022 A253023

Keyword

nonn

Author

R. H. Hardin, Dec 26 2014

Status

approved