A281199 - OEIS

%I #7 Feb 16 2019 11:14:28

%S 0,2,10,38,130,420,1308,3970,11822,34690,100610,289032,823800,2332418,

%T 6566290,18394910,51310978,142587180,394905492,1090444930,3002921270,

%U 8249479162,22612505090,61857842448,168903452400,460409998850

%N Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281199/b281199.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

%F Conjectures from _Colin Barker_, Feb 16 2019: (Start)

%F G.f.: 2*x^2*(1 - x) / (1 - 3*x + x^2)^2.

%F a(n) = (2^(-n)*(2*sqrt(5)*((3-sqrt(5))^n - (3+sqrt(5))^n) - 5*(3-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(3+sqrt(5))^n*n)) / 25.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A281205.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 17 2017