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Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
1

%I #4 Mar 11 2017 08:13:02

%S 1,26,169,1108,6453,36038,194173,1021432,5275885,26869458,135310457,

%T 675163708,3343196861,16447661790,80470971869,391822686752,

%U 1899839181365,9177752354378,44190339947417,212148874972196,1015791721800101

%N Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%C Column 3 of A283572.

%H R. H. Hardin, <a href="/A283567/b283567.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -27*a(n-2) -4*a(n-3) +89*a(n-4) -106*a(n-5) -85*a(n-6) +228*a(n-7) -60*a(n-8) -192*a(n-9) +144*a(n-10) +64*a(n-11) -64*a(n-12)

%e Some solutions for n=4

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

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

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

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

%Y Cf. A283572.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 11 2017