A251276 - OEIS

%I #7 Nov 27 2018 12:25:41

%S 230,3264,46244,655040,9278296,131421696,1861511440,26367218944,

%T 373476205664,5290071598080,74930764222016,1061350366002176,

%U 15033405986262400,212939386264141824,3016161624583446784

%N Number of (n+1) X (1+1) 0..3 arrays with no 2 X 2 subblock having its maximum diagonal element less than its minimum antidiagonal element.

%H R. H. Hardin, <a href="/A251276/b251276.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) - 26*a(n-2).

%F Conjectures from _Colin Barker_, Nov 27 2018: (Start)

%F G.f.: 2*x*(115 - 208*x) / (1 - 16*x + 26*x^2).

%F a(n) = ((8-sqrt(38))^n*(-51+8*sqrt(38)) + (8+sqrt(38))^n*(51+8*sqrt(38))) / sqrt(38).

%F (End)

%e Some solutions for n=3:

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

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

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

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

%Y Column 1 of A251283.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014