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A268628 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

%I A268628 #4 Feb 09 2016 09:24:58
%S A268628 3,9,9,24,42,24,60,174,174,60,144,666,1086,666,144,336,2430,6300,6300,
%T A268628 2430,336,768,8586,34890,55452,34890,8586,768,1728,29646,187224,
%U A268628 467190,467190,187224,29646,1728,3840,100602,982086,3819654,6000978,3819654
%N A268628 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
%C A268628 Table starts
%C A268628 ....3.......9........24..........60...........144.............336
%C A268628 ....9......42.......174.........666..........2430............8586
%C A268628 ...24.....174......1086........6300.........34890..........187224
%C A268628 ...60.....666......6300.......55452........467190.........3819654
%C A268628 ..144....2430.....34890......467190.......6000978........74914554
%C A268628 ..336....8586....187224.....3819654......74914554......1430057208
%C A268628 ..768...29646....982086....30553014.....915847266.....26758514760
%C A268628 .1728..100602...5063964...240364746...11018667294....493042858032
%C A268628 .3840..336798..25764066..1866503592..130903914954...8974328440044
%C A268628 .8448.1115370.129678528.14342680944.1539375100362.161737670836314
%H A268628 R. H. Hardin, <a href="/A268628/b268628.txt">Table of n, a(n) for n = 1..420</a>
%F A268628 Empirical for column k:
%F A268628 k=1: a(n) = 4*a(n-1) -4*a(n-2)
%F A268628 k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
%F A268628 k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4)
%F A268628 k=4: [order 6] for n>7
%F A268628 k=5: [order 10]
%F A268628 k=6: [order 14] for n>15
%F A268628 k=7: [order 26]
%e A268628 Some solutions for n=4 k=4
%e A268628 ..2..1..0..0. .1..2..1..0. .0..0..0..0. .1..2..2..2. .0..0..0..1
%e A268628 ..1..0..0..0. .0..1..0..0. .0..0..0..0. .2..1..2..2. .0..0..1..0
%e A268628 ..2..0..1..0. .1..0..0..0. .1..0..0..0. .1..2..2..2. .0..0..0..1
%e A268628 ..2..1..0..1. .0..0..1..1. .2..1..1..0. .0..2..2..2. .0..1..1..2
%Y A268628 Column 1 is A084858.
%K A268628 nonn,tabl
%O A268628 1,1
%A A268628 _R. H. Hardin_, Feb 09 2016