login
Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.
1

%I #6 Mar 02 2017 12:33:27

%S 0,2,8,32,122,416,1414,4626,14930,47432,149032,463918,1432956,4397436,

%T 13419434,40754026,123245234,371322718,1115052844,3338521720,

%U 9969125698,29697147320,88271949298,261856896380,775373941754,2292071140404

%N Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.

%C Column 2 of A282885.

%H R. H. Hardin, <a href="/A282879/b282879.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) -2*a(n-3) -20*a(n-4) -24*a(n-5) -19*a(n-6) -14*a(n-7) -7*a(n-8) -2*a(n-9) -a(n-10).

%F Empirical: G.f.: 2*x^2*(2*x+1)*(x^3+x^2+1) / ( (x^5+x^4+3*x^3+4*x^2+x-1)^2 ). - _R. J. Mathar_, Mar 02 2017

%e Some solutions for n=4

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

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

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

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

%Y Cf. A282885.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 24 2017