A252713 Number of (n+2) X (2+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

52, 46, 56, 76, 102, 154, 220, 306, 478, 700, 990, 1570, 2332, 3330, 5326, 7996, 11502, 18514, 28060, 40626, 65758, 100540, 146430, 238210, 367132, 537570, 878446, 1363516, 2005902, 3290674, 5139100, 7590546, 12493438, 19611580, 29063070

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 7*a(n-3) - 7*a(n-4) - 12*a(n-6) + 12*a(n-7) for n>9.

Empirical g.f.: 2*x*(26 - 3*x + 5*x^2 - 172*x^3 + 34*x^4 - 9*x^5 + 275*x^6 - 84*x^7 - 36*x^8) / ((1 - x)*(1 - 3*x^3)*(1 - 4*x^3)). - Colin Barker, Dec 05 2018

Example

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

Crossrefs

Column 2 of A252719.

Sequence in context: A033372 A126767 A143723 * A249404 A327374 A327109

Adjacent sequences: A252710 A252711 A252712 * A252714 A252715 A252716

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved