A252712 - OEIS

%I #8 Dec 05 2018 09:36:17

%S 39,45,54,84,111,165,257,376,560,930,1365,2091,3503,5206,8006,13536,

%T 20163,31137,52829,78868,122012,207582,310257,480663,819275,1225618,

%U 1900658,3244188,4856415,7536909,12878201,19287760,29950664,51217434

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

%H R. H. Hardin, <a href="/A252712/b252712.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(39 + 6*x - 30*x^2 - 249*x^3 - 24*x^4 + 234*x^5 + 365*x^6 + 11*x^7 - 436*x^8 + 84*x^9 + 12*x^10) / ((1 - x)^2*(1 + x)*(1 - 3*x^3)*(1 - 4*x^3)). - _Colin Barker_, Dec 05 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A252719.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2014