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A275266 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-1) and new values introduced in order 0..2. 13

%I #4 Jul 21 2016 11:34:54

%S 1,2,2,5,9,5,14,54,24,14,41,324,128,64,41,122,1944,688,396,172,122,

%T 365,11664,3728,2564,1440,476,365,1094,69984,20224,17036,13156,5676,

%U 1320,1094,3281,419904,109760,114184,126420,73012,22844,3672,3281,9842

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-1) and new values introduced in order 0..2.

%C Table starts

%C ....1.....2.......5.......14.........41..........122............365

%C ....2.....9......54......324.......1944........11664..........69984

%C ....5....24.....128......688.......3728........20224.........109760

%C ...14....64.....396.....2564......17036.......114184.........767400

%C ...41...172....1440....13156.....126420......1224088.......11894712

%C ..122...476....5676....73012....1020324.....14005180......194398028

%C ..365..1320...22844...409728....8391716....161725644.....3224773976

%C .1094..3672...93968..2315520...70863268...1922952988....56045462432

%C .3281.10220..389820.13124196..603245904..22903224024...981633748272

%C .9842.28472.1626348.74374784.5149743348.271600215464.17187870741644

%H R. H. Hardin, <a href="/A275266/b275266.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2)

%F k=2: [order 9] for n>10

%F k=3: [order 14] for n>17

%F k=4: [order 43] for n>47

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -3*a(n-2)

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

%F n=3: a(n) = 6*a(n-1) -2*a(n-2) -6*a(n-3) for n>4

%F n=4: a(n) = 8*a(n-1) -7*a(n-2) -9*a(n-3) -8*a(n-4) -12*a(n-5) +16*a(n-6) for n>7

%F n=5: [order 18] for n>19

%F n=6: [order 24] for n>26

%F n=7: [order 43] for n>45

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A007051(n-1).

%Y Row 1 is A007051(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 21 2016

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)