A252691 - OEIS

A252691

Number of (n+2) X (4+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

394, 519, 407, 1480, 2048, 6246, 12740, 35128, 84680, 225000, 573968, 1508116, 3915680, 10257360, 26778908, 70099888, 183333200, 479875356, 1255786736, 3287174320, 8604199916, 22523755824, 58961898416, 154354406332, 404082593744

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 11*a(n-3) + 9*a(n-4) + 12*a(n-5) + 12*a(n-6) - 34*a(n-7) - 8*a(n-8) + 28*a(n-9) - 8*a(n-10) for n>11.

Empirical g.f.: x*(394 - 1451*x - 612*x^2 + 5855*x^3 - 1561*x^4 - 2996*x^5 - 8637*x^6 + 7904*x^7 + 8428*x^8 - 9340*x^9 + 2104*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x + x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Dec 05 2018

EXAMPLE

Some solutions for n=4:

..0..1..1..0..0..2....0..0..1..1..0..1....0..1..1..2..2..3....0..1..1..2..2..1

..0..2..2..3..3..2....2..3..2..3..2..3....2..3..3..0..0..1....2..3..3..0..0..3

..3..1..1..0..0..1....2..3..2..3..2..3....0..1..1..2..2..3....2..1..1..2..2..3

..0..2..2..3..3..1....0..1..0..1..0..1....0..3..3..0..0..1....0..3..3..0..0..1

..3..1..1..0..0..2....0..1..0..1..0..1....2..1..1..2..2..1....2..1..1..2..2..3

..3..2..2..3..3..2....2..2..3..2..3..2....0..3..3..0..0..3....0..3..3..0..0..3

CROSSREFS

Column 4 of A252695.

Sequence in context: A172931 A172710 A236234 * A051986 A223908 A251256

Adjacent sequences: A252688 A252689 A252690 * A252692 A252693 A252694

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 20 2014

STATUS

approved