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Number of n X 3 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
1

%I #6 May 09 2021 20:39:14

%S 0,3,16,66,351,1758,9033,46159,236245,1208622,6183942,31638994,

%T 161877345,828222749,4237494527,21680576851,110925816281,567537279930,

%U 2903729582172,14856548980595,76011571374458,388903168793624

%N Number of n X 3 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%C Column 3 of A278094.

%H R. H. Hardin, <a href="/A278089/b278089.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +14*a(n-2) -9*a(n-3) -44*a(n-4) +21*a(n-5) +83*a(n-6) -19*a(n-7) -81*a(n-8) +a(n-9) +17*a(n-10) -10*a(n-11) +4*a(n-12) +5*a(n-13) for n > 16.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A278094.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 11 2016