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A253018 Number of (n+2) X (1+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 #8 Dec 08 2018 06:45:38

%S 25,37,51,63,105,153,189,315,459,567,945,1377,1701,2835,4131,5103,

%T 8505,12393,15309,25515,37179,45927,76545,111537,137781,229635,334611,

%U 413343,688905,1003833,1240029,2066715,3011499,3720087,6200145,9034497,11160261

%N Number of (n+2) X (1+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="/A253018/b253018.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-3) for n>5.

%F Empirical g.f.: x*(25 + 37*x + 51*x^2 - 12*x^3 - 6*x^4) / (1 - 3*x^3). - _Colin Barker_, Dec 08 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A253025.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2014

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Last modified July 12 14:24 EDT 2024. Contains 374251 sequences. (Running on oeis4.)