A252693 Number of (n+2) X (6+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

1982, 2719, 881, 6246, 4138, 18940, 25382, 82842, 168598, 474106, 1144322, 3060306, 7815922, 20586466, 53494154, 140277762, 366408034, 959644570, 2510532578, 6573087906, 17204221018, 45040796194, 117907050914, 308678604858

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 11*a(n-3) + 9*a(n-4) + 12*a(n-5) + 12*a(n-6) - 34*a(n-7) - 8*a(n-8) + 28*a(n-9) - 8*a(n-10) for n>11.

Empirical g.f.: x*(1982 - 7191*x - 4786*x^2 + 34519*x^3 - 11497*x^4 - 15330*x^5 - 48401*x^6 + 45184*x^7 + 49792*x^8 - 57172*x^9 + 13208*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x + x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 6 of A252695.

Sequence in context: A035870 A345517 A345770 * A166876 A028238 A022063

Adjacent sequences: A252690 A252691 A252692 * A252694 A252695 A252696

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved