A252378 Number of (n+2) X (2+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.

897, 555, 529, 570, 637, 764, 903, 1117, 1470, 1843, 2410, 3329, 4304, 5795, 8196, 10747, 14657, 20938, 27615, 37858, 54297, 71776, 98599, 141632, 187391, 257621, 370278, 490075, 673946, 968881, 1282512, 1763899, 2536044, 3357139, 4617433

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-3) - 4*a(n-6) + a(n-9) for n>15.

Empirical g.f.: x*(897 + 555*x + 529*x^2 - 3018*x^3 - 1583*x^4 - 1352*x^5 + 2211*x^6 + 789*x^7 + 530*x^8 - 386*x^9 - 65*x^10 - 24*x^11 - 26*x^12 - 14*x^13 - 4*x^14) / ((1 - x)*(1 + x + x^2)*(1 - 3*x^3 + x^6)). - Colin Barker, Dec 03 2018

Example

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

Crossrefs

Column 2 of A252384.

Sequence in context: A287944 A323964 A145498 * A210129 A158408 A158409

Adjacent sequences: A252375 A252376 A252377 * A252379 A252380 A252381

Keyword

nonn

Author

R. H. Hardin, Dec 17 2014

Status

approved