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A253019 Number of (n+2) X (2+2) 0..3 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order. 1

%I

%S 37,50,83,91,133,223,243,357,595,653,959,1589,1761,2583,4253,4765,

%T 6979,11413,12939,18921,30715,35267,51485,82919,96507,140637,224603,

%U 265189,385735,610573,731865,1062495,1666165,2028821,2939531,4565069,5649843

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

%H R. H. Hardin, <a href="/A253019/b253019.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-3) -10*a(n-6) +3*a(n-9) for n>11.

%F Empirical g.f.: x*(37 + 50*x + 83*x^2 - 131*x^3 - 167*x^4 - 275*x^5 + 67*x^6 + 59*x^7 + 87*x^8 - 6*x^9 - 3*x^10) / ((1 - 3*x^3)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Dec 08 2018

%e Some solutions for n=4:

%e ..0..1..2..0....0..0..0..0....0..0..0..0....0..0..0..0....0..1..2..0

%e ..2..2..2..2....1..2..0..1....1..2..0..3....1..0..2..1....3..0..2..3

%e ..3..0..2..1....2..1..0..2....2..1..0..2....2..0..1..2....2..2..2..2

%e ..0..3..2..0....0..0..0..0....0..0..0..0....0..0..0..0....0..3..2..0

%e ..2..2..2..2....1..2..0..1....1..2..0..1....1..0..2..1....3..0..2..1

%e ..1..0..2..3....2..3..0..2....2..3..0..2....2..0..1..2....2..2..2..2

%Y Column 2 of A253025.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2014

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Last modified October 24 15:56 EDT 2021. Contains 348233 sequences. (Running on oeis4.)