A252132 Number of (n+2) X (1+2) 0..3 arrays with every 3 X 3 subblock row, column, diagonal and antidiagonal sum not equal to 0 3 4 6 or 7.

172, 134, 209, 439, 909, 1864, 3905, 8406, 18168, 39279, 85291, 186213, 407616, 893115, 1958970, 4302138, 9455841, 20792427, 45735313, 100630844, 221468341, 487479454, 1073112928, 2362493679, 5201444067, 11452406745, 25216409792

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(172 - 210*x - 231*x^2 - 113*x^3 - 350*x^4 + 333*x^5 + 933*x^6 + 792*x^7 - 86*x^8 - 650*x^9 - 324*x^10 - 32*x^11) / ((1 - x)*(1 + x)*(1 - x - x^2)*(1 - x - 3*x^3 - 4*x^4 - 4*x^5 - 2*x^6)). - Colin Barker, Dec 01 2018

Example

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

Crossrefs

Column 1 of A252139.

Sequence in context: A015356 A259158 A252139 * A252131 A223823 A224555

Adjacent sequences: A252129 A252130 A252131 * A252133 A252134 A252135

Keyword

nonn

Author

R. H. Hardin, Dec 14 2014

Status

approved