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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. 8

%I

%S 3,9,9,24,42,24,60,174,174,60,144,666,1086,666,144,336,2430,6300,6300,

%T 2430,336,768,8586,34890,55452,34890,8586,768,1728,29646,187224,

%U 467190,467190,187224,29646,1728,3840,100602,982086,3819654,6000978,3819654

%N 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 Table starts

%C ....3.......9........24..........60...........144.............336

%C ....9......42.......174.........666..........2430............8586

%C ...24.....174......1086........6300.........34890..........187224

%C ...60.....666......6300.......55452........467190.........3819654

%C ..144....2430.....34890......467190.......6000978........74914554

%C ..336....8586....187224.....3819654......74914554......1430057208

%C ..768...29646....982086....30553014.....915847266.....26758514760

%C .1728..100602...5063964...240364746...11018667294....493042858032

%C .3840..336798..25764066..1866503592..130903914954...8974328440044

%C .8448.1115370.129678528.14342680944.1539375100362.161737670836314

%H R. H. Hardin, <a href="/A268628/b268628.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -4*a(n-2)

%F k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3

%F k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4)

%F k=4: [order 6] for n>7

%F k=5: [order 10]

%F k=6: [order 14] for n>15

%F k=7: [order 26]

%e Some solutions for n=4 k=4

%e ..2..1..0..0. .1..2..1..0. .0..0..0..0. .1..2..2..2. .0..0..0..1

%e ..1..0..0..0. .0..1..0..0. .0..0..0..0. .2..1..2..2. .0..0..1..0

%e ..2..0..1..0. .1..0..0..0. .1..0..0..0. .1..2..2..2. .0..0..0..1

%e ..2..1..0..1. .0..0..1..1. .2..1..1..0. .0..2..2..2. .0..1..1..2

%Y Column 1 is A084858.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 09 2016

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Last modified May 23 07:19 EDT 2022. Contains 353961 sequences. (Running on oeis4.)