A268639 - OEIS

%I #4 Feb 09 2016 12:23:51

%S 0,3,3,12,24,12,36,120,120,36,96,504,840,504,96,240,1944,5178,5178,

%T 1944,240,576,7128,29772,47640,29772,7128,576,1344,25272,163878,

%U 412740,412740,163878,25272,1344,3072,87480,875592,3440052,5419992,3440052,875592

%N T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

%C Table starts

%C ....0......3........12..........36............96.............240

%C ....3.....24.......120.........504..........1944............7128

%C ...12....120.......840........5178.........29772..........163878

%C ...36....504......5178.......47640........412740.........3440052

%C ...96...1944.....29772......412740.......5419992........68710116

%C ..240...7128....163878.....3440052......68710116......1328460312

%C ..576..25272....875592....27906474.....849572724.....25093766490

%C .1344..87480...4578186...221913216...10310685036....465757993812

%C .3072.297432..23548164..1737860310..123340687488...8527096170390

%C .6912.997272.119570574.13445785116.1458578214948.154406753980596

%H R. H. Hardin, <a href="/A268639/b268639.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..0..0..0. .2..2..1..0. .0..0..0..0. .2..1..2..2. .0..1..2..2

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

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

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

%Y Column 1 is A167667(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 09 2016