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A269109 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

%I A269109 #4 Feb 19 2016 13:48:23
%S A269109 4,16,16,60,180,60,216,1740,1740,216,756,15540,40908,15540,756,2592,
%T A269109 132300,872460,872460,132300,2592,8748,1090740,17593092,43964700,
%U A269109 17593092,1090740,8748,29160,8787660,342055548,2085484068,2085484068
%N A269109 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.
%C A269109 Table starts
%C A269109 ......4.........16.............60................216....................756
%C A269109 .....16........180...........1740..............15540.................132300
%C A269109 .....60.......1740..........40908.............872460...............17593092
%C A269109 ....216......15540.........872460...........43964700.............2085484068
%C A269109 ....756.....132300.......17593092.........2085484068...........232068730044
%C A269109 ...2592....1090740......342055548........95166487524.........24808345933548
%C A269109 ...8748....8787660.....6482020140......4227147007836.......2579398703502996
%C A269109 ..29160...69580980...120520189980....184069947098892.....262780733311913580
%C A269109 ..96228..543538380..2208175854948...7894012975085748...26357371124964908460
%C A269109 .314928.4200069300.39988864047276.334480929126425748.2611360040338484328156
%H A269109 R. H. Hardin, <a href="/A269109/b269109.txt">Table of n, a(n) for n = 1..264</a>
%F A269109 Empirical for column k:
%F A269109 k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F A269109 k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
%F A269109 k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5
%F A269109 k=4: [order 6] for n>7
%F A269109 k=5: [order 14] for n>15
%F A269109 k=6: [order 26] for n>27
%F A269109 k=7: [order 64] for n>65
%e A269109 Some solutions for n=3 k=4
%e A269109 ..0..0..1..2. .0..2..2..0. .0..1..1..1. .0..2..3..1. .2..0..1..0
%e A269109 ..0..2..3..3. .0..2..0..1. .0..0..3..1. .0..0..1..3. .0..0..1..1
%e A269109 ..1..3..1..3. .1..0..0..2. .0..2..2..3. .0..0..0..2. .2..2..2..3
%Y A269109 Column 1 is A120926(n+1).
%K A269109 nonn,tabl
%O A269109 1,1
%A A269109 _R. H. Hardin_, Feb 19 2016