A253021 Number of (n+2) X (4+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.

63, 91, 120, 155, 230, 296, 369, 546, 712, 893, 1322, 1722, 2155, 3190, 4158, 5203, 7702, 10040, 12561, 18594, 24240, 30325, 44890, 58522, 73211, 108374, 141286, 176747, 261638, 341096, 426705, 631650, 823480, 1030157, 1524938, 1988058

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(63 + 91*x + 120*x^2 - 34*x^3 - 43*x^4 - 64*x^5 - 33*x^6 - 53*x^7 - 56*x^8 + 4*x^9 + 5*x^10 + 2*x^11) / ((1 - x)*(1 + x + x^2)*(1 - 2*x^3 - x^6)). - Colin Barker, Dec 08 2018

Example

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

Crossrefs

Column 4 of A253025.

Sequence in context: A062375 A343025 A343003 * A039480 A023688 A118157

Adjacent sequences: A253018 A253019 A253020 * A253022 A253023 A253024

Keyword

nonn

Author

R. H. Hardin, Dec 26 2014

Status

approved