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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. 8

%I

%S 4,16,16,60,180,60,216,1740,1740,216,756,15540,40908,15540,756,2592,

%T 132300,872460,872460,132300,2592,8748,1090740,17593092,43964700,

%U 17593092,1090740,8748,29160,8787660,342055548,2085484068,2085484068

%N 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 Table starts

%C ......4.........16.............60................216....................756

%C .....16........180...........1740..............15540.................132300

%C .....60.......1740..........40908.............872460...............17593092

%C ....216......15540.........872460...........43964700.............2085484068

%C ....756.....132300.......17593092.........2085484068...........232068730044

%C ...2592....1090740......342055548........95166487524.........24808345933548

%C ...8748....8787660.....6482020140......4227147007836.......2579398703502996

%C ..29160...69580980...120520189980....184069947098892.....262780733311913580

%C ..96228..543538380..2208175854948...7894012975085748...26357371124964908460

%C .314928.4200069300.39988864047276.334480929126425748.2611360040338484328156

%H R. H. Hardin, <a href="/A269109/b269109.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

%F k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3

%F k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5

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

%F k=5: [order 14] for n>15

%F k=6: [order 26] for n>27

%F k=7: [order 64] for n>65

%e Some solutions for n=3 k=4

%e ..0..0..1..2. .0..2..2..0. .0..1..1..1. .0..2..3..1. .2..0..1..0

%e ..0..2..3..3. .0..2..0..1. .0..0..3..1. .0..0..1..3. .0..0..1..1

%e ..1..3..1..3. .1..0..0..2. .0..2..2..3. .0..0..0..2. .2..2..2..3

%Y Column 1 is A120926(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 19 2016

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Last modified May 13 16:56 EDT 2021. Contains 343862 sequences. (Running on oeis4.)