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A268809 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

%I A268809 #4 Feb 13 2016 18:23:47
%S A268809 3,9,9,24,34,24,60,104,104,60,144,290,332,290,144,336,772,1202,1202,
%T A268809 772,336,768,1972,4158,5848,4158,1972,768,1728,4914,14308,28452,28452,
%U A268809 14308,4914,1728,3840,12010,48460,135912,195384,135912,48460,12010,3840,8448
%N A268809 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.
%C A268809 Table starts
%C A268809 ....3.....9......24.......60........144.........336...........768
%C A268809 ....9....34.....104......290........772........1972..........4914
%C A268809 ...24...104.....332.....1202.......4158.......14308.........48460
%C A268809 ...60...290....1202.....5848......28452......135912........640926
%C A268809 ..144...772....4158....28452.....195384.....1316226.......8734264
%C A268809 ..336..1972...14308...135912....1316226....12432856.....115671422
%C A268809 ..768..4914...48460...640926....8734264...115671422....1508087180
%C A268809 .1728.12010..162722..2990786...57302798..1062318610...19390335102
%C A268809 .3840.28922..541744.13835892..372342650..9657289546..246666802206
%C A268809 .8448.68836.1791504.63544542.2400532536.87052567448.3110082281974
%H A268809 R. H. Hardin, <a href="/A268809/b268809.txt">Table of n, a(n) for n = 1..637</a>
%F A268809 Empirical for column k:
%F A268809 k=1: a(n) = 4*a(n-1) -4*a(n-2)
%F A268809 k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>7
%F A268809 k=3: [order 10] for n>12
%F A268809 k=4: [order 16] for n>19
%F A268809 k=5: [order 26] for n>29
%F A268809 k=6: [order 42] for n>45
%F A268809 k=7: [order 68] for n>71
%e A268809 Some solutions for n=4 k=4
%e A268809 ..1..2..1..2. .1..0..0..0. .2..2..1..2. .2..1..0..1. .2..2..1..2
%e A268809 ..1..2..2..2. .0..0..1..0. .1..2..2..2. .0..0..0..0. .1..2..1..2
%e A268809 ..2..2..2..1. .0..0..0..1. .2..1..2..1. .0..1..0..0. .2..2..2..2
%e A268809 ..2..2..2..2. .0..0..0..0. .2..2..1..2. .0..0..0..0. .2..2..1..2
%Y A268809 Column 1 is A084858.
%K A268809 nonn,tabl
%O A268809 1,1
%A A268809 _R. H. Hardin_, Feb 13 2016