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A275139 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

%I A275139 #8 Jan 31 2019 19:36:47
%S A275139 8,144,528,2320,9744,41360,175120,741904,3142672,13312656,56393232,
%T A275139 238885648,1011935760,4286628752,18158450704,76920431632,325840177168,
%U A275139 1380281140368,5846964738576,24768140094736,104919525117456
%N A275139 Number of n X 5 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.
%H A275139 R. H. Hardin, <a href="/A275139/b275139.txt">Table of n, a(n) for n = 1..210</a>
%F A275139 Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3) for n>4.
%F A275139 Conjectures from _Colin Barker_, Jan 31 2019: (Start)
%F A275139 G.f.: 8*x*(1 + 15*x + 7*x^2 + x^3) / ((1 + x)*(1 - 4*x - x^2)).
%F A275139 a(n) = 8*(2*(-1)^n - (2*((2-sqrt(5))^n - (2+sqrt(5))^n))/sqrt(5)) for n>1.
%F A275139 (End)
%e A275139 Some solutions for n=5:
%e A275139 ..0..1..2..1..0. .0..1..0..2..1. .0..1..0..1..0. .0..1..2..1..2
%e A275139 ..2..1..2..0..1. .1..2..1..0..1. .2..1..2..0..2. .0..1..2..0..1
%e A275139 ..2..0..1..2..1. .1..0..2..0..2. .2..0..1..2..1. .2..0..1..0..1
%e A275139 ..1..0..1..2..0. .2..1..2..1..0. .1..0..1..2..0. .2..0..1..2..0
%e A275139 ..1..2..0..2..0. .2..1..0..2..0. .1..2..0..1..0. .2..1..0..2..0
%Y A275139 Column 5 of A275142.
%K A275139 nonn
%O A275139 1,1
%A A275139 _R. H. Hardin_, Jul 17 2016