A252724 Number of (5+2) X (n+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.

111, 102, 119, 135, 147, 191, 211, 251, 323, 375, 447, 599, 691, 851, 1139, 1335, 1647, 2231, 2611, 3251, 4403, 5175, 6447, 8759, 10291, 12851, 17459, 20535, 25647, 34871, 41011, 51251, 69683, 81975, 102447, 139319, 163891, 204851, 278579, 327735

Offset

1,1

Links

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

Formula

Empirical: a(n) = -a(n-1) + 3*a(n-3) + 3*a(n-4) - 2*a(n-6) - 2*a(n-7) for n>9.

Empirical g.f.: x*(111 + 213*x + 221*x^2 - 79*x^3 - 357*x^4 - 325*x^5 - 138*x^6 + 42*x^7 + 2*x^8) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - 2*x^3)). - Colin Barker, Dec 06 2018

Example

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

Crossrefs

Row 5 of A252719.

Sequence in context: A072807 A282976 A284083 * A073502 A066335 A107844

Adjacent sequences: A252721 A252722 A252723 * A252725 A252726 A252727

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved