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A274723 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

%I A274723 #8 Jan 30 2019 09:09:24
%S A274723 5,24,68,260,1040,4132,16524,66088,264332,1057316,4229264,16917028,
%T A274723 67668108,270672424,1082689676,4330758692,17323034768,69292139044,
%U A274723 277168556172,1108674224680,4434696898700,17738787594788,70955150379152
%N A274723 Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.
%H A274723 R. H. Hardin, <a href="/A274723/b274723.txt">Table of n, a(n) for n = 1..210</a>
%F A274723 Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3) - 3*a(n-4) - 4*a(n-5) for n>7.
%F A274723 Empirical g.f.: x*(5 + 9*x - 24*x^2 - 45*x^3 - 21*x^4 - 4*x^5 + 8*x^6) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 + x + x^2)). - _Colin Barker_, Jan 30 2019
%e A274723 Some solutions for n=4:
%e A274723 ..0..1..0. .0..0..0. .0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..0
%e A274723 ..1..0..1. .1..1..1. .1..0..1. .2..0..2. .2..0..2. .1..2..1. .1..2..1
%e A274723 ..0..1..2. .2..2..2. .2..1..0. .0..1..0. .1..2..0. .2..1..2. .2..1..2
%e A274723 ..1..2..1. .0..0..0. .0..0..1. .2..0..2. .0..0..2. .0..2..0. .1..0..1
%Y A274723 Column 3 of A274728.
%K A274723 nonn
%O A274723 1,1
%A A274723 _R. H. Hardin_, Jul 03 2016