A253019 Number of (n+2) X (2+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.

37, 50, 83, 91, 133, 223, 243, 357, 595, 653, 959, 1589, 1761, 2583, 4253, 4765, 6979, 11413, 12939, 18921, 30715, 35267, 51485, 82919, 96507, 140637, 224603, 265189, 385735, 610573, 731865, 1062495, 1666165, 2028821, 2939531, 4565069, 5649843

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-3) -10*a(n-6) +3*a(n-9) for n>11.

Empirical g.f.: x*(37 + 50*x + 83*x^2 - 131*x^3 - 167*x^4 - 275*x^5 + 67*x^6 + 59*x^7 + 87*x^8 - 6*x^9 - 3*x^10) / ((1 - 3*x^3)*(1 - 3*x^3 + x^6)). - Colin Barker, Dec 08 2018

Example

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

Crossrefs

Column 2 of A253025.

Sequence in context: A162556 A129072 A297911 * A298504 A074401 A323476

Adjacent sequences: A253016 A253017 A253018 * A253020 A253021 A253022

Keyword

nonn

Author

R. H. Hardin, Dec 26 2014

Status

approved