A251645 Number of (n+2) X (1+2) 0..3 arrays with no row, column, diagonal or antidiagonal in any 3 X 3 subblock summing to 0 2 4 5 7 or 9.

376, 448, 738, 1248, 2382, 4140, 6978, 13532, 23574, 39904, 78046, 136408, 231290, 455168, 797254, 1353500, 2675622, 4693960, 7976098, 15819328, 27784502, 47242988, 93923158, 165100664, 280858818, 559333552, 983799526, 1674143116

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 5*a(n-3) - 7*a(n-4) - 12*a(n-5) + 6*a(n-6) + 6*a(n-7) for n>14.

Empirical g.f.: 2*x*(188 + 36*x - 231*x^2 - 1133*x^3 + 25*x^4 + 1610*x^5 + 60*x^6 - 494*x^7 - 40*x^8 + 12*x^9 + 40*x^10 + 6*x^11 - 18*x^12 - 6*x^13) / ((1 - x)*(1 + x)*(1 - x - x^2)*(1 - 6*x^3)). - Colin Barker, Nov 30 2018

Example

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

Crossrefs

Column 1 of A251652.

Sequence in context: A252071 A247263 A251652 * A259769 A238231 A008853

Adjacent sequences: A251642 A251643 A251644 * A251646 A251647 A251648

Keyword

nonn

Author

R. H. Hardin, Dec 06 2014

Status

approved