login
Number of nX2 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
8

%I #4 Feb 03 2017 08:19:43

%S 2,8,30,112,420,1576,5912,22176,83184,312032,1170464,4390528,16469312,

%T 61778048,231735680,869263872,3260696320,12231200256,45880463872,

%U 172102240256,645572834304,2421608712192,9083698141184,34073866477568

%N Number of nX2 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%C Column 2 of A281955.

%H R. H. Hardin, <a href="/A281949/b281949.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281955.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2017