A231445 - OEIS

%I #9 Sep 29 2018 03:12:11

%S 3,15,97,715,5643,46075,382341,3196783,26821757,225400759,1895576427,

%T 15946759047,134174450017,1129009038167,9500331770337,79944094951011,

%U 672723905279179,5660941011339603,47636625510849789,400860827109560351

%N Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..3 introduced in row major order.

%H R. H. Hardin, <a href="/A231445/b231445.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-1) - 133*a(n-2) + 461*a(n-3) - 867*a(n-4) + 881*a(n-5) - 468*a(n-6) + 108*a(n-7).

%F Empirical g.f.: x*(3 - 42*x + 211*x^2 - 516*x^3 + 645*x^4 - 402*x^5 + 108*x^6) / ((1 - x)*(1 - 5*x + 5*x^2 - 2*x^3)*(1 - 13*x + 45*x^2 - 54*x^3)). - _Colin Barker_, Sep 29 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

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

%Y Column 2 of A231451.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2013