A275504 - OEIS

%I #4 Jul 30 2016 20:00:58

%S 1,2,2,5,9,3,14,54,16,6,41,324,80,28,12,122,1944,400,136,56,24,365,

%T 11664,2000,656,232,104,48,1094,69984,10000,3168,988,516,200,96,3281,

%U 419904,50000,15296,4180,2628,1168,380,192,9842,2519424,250000,73856,17712

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

%C Table starts

%C ...1....2.....5.....14......41......122.......365.......1094........3281

%C ...2....9....54....324....1944....11664.....69984.....419904.....2519424

%C ...3...16....80....400....2000....10000.....50000.....250000.....1250000

%C ...6...28...136....656....3168....15296.....73856.....356608.....1721856

%C ..12...56...232....988....4180....17712.....75024.....317812.....1346268

%C ..24..104...516...2628...13384....68080....346528....1763408.....8974288

%C ..48..200..1168...7140...43780...268152...1643372...10069540....61703488

%C ..96..380..2660..19368..143784..1063756...7886280...58423188...432942008

%C .192..724..6024..52864..470352..4220952..37846556..339516412..3045734096

%C .384.1380.13716.144228.1549756.16808164.182923008.1989999904.21655912500

%H R. H. Hardin, <a href="/A275504/b275504.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 2*a(n-1) +2*a(n-2) -2*a(n-3) -4*a(n-4) +3*a(n-5) +a(n-6) -a(n-7) for n>11

%F k=4: [order 16] for n>20

%F k=5: [order 32] for n>36

%F k=6: [order 64] for n>68

%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) = 5*a(n-1) for n>2

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

%F n=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3)

%F n=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>5

%F n=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>6

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A003945(n-2).

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

%Y Row 3 is A055842.

%Y Row 4 is A108051(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 30 2016