Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Jul 04 2016 10:19:04
%S 1,1,1,2,3,2,4,8,9,4,8,22,34,27,8,16,60,133,144,81,16,32,164,518,813,
%T 610,243,32,64,448,2017,4554,4967,2584,729,64,128,1224,7858,25585,
%U 40242,30349,10946,2187,128,256,3344,30605,143634,327123,355504,185435,46368
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.
%C Table starts
%C ...1.....1......2........4..........8...........16............32
%C ...1.....3......8.......22.........60..........164...........448
%C ...2.....9.....34......133........518.........2017..........7858
%C ...4....27....144......813.......4554........25585........143634
%C ...8....81....610.....4967......40242.......327123.......2661918
%C ..16...243...2584....30349.....355504......4190533......49475642
%C ..32...729..10946...185435....3140840.....53680592.....920432562
%C ..64..2187..46368..1133025...27748676....687685512...17123659885
%C .128..6561.196418..6922887..245154340...8809672678..318581114142
%C .256.19683.832040.42299477.2165891856.112857546696.5927090659144
%H R. H. Hardin, <a href="/A274749/b274749.txt">Table of n, a(n) for n = 1..363</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) for n>2
%F k=2: a(n) = 3*a(n-1)
%F k=3: a(n) = 4*a(n-1) +a(n-2)
%F k=4: a(n) = 6*a(n-1) +a(n-2) -2*a(n-3) for n>4
%F k=5: a(n) = 9*a(n-1) -14*a(n-3) +10*a(n-4) -2*a(n-5) for n>6
%F k=6: [order 9] for n>11
%F k=7: [order 13] for n>15
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) for n>2
%F n=2: a(n) = 2*a(n-1) +2*a(n-2)
%F n=3: a(n) = 2*a(n-1) +7*a(n-2) +2*a(n-3) -2*a(n-4)
%F n=4: [order 8]
%F n=5: [order 16] for n>17
%F n=6: [order 36] for n>38
%F n=7: [order 80] for n>83
%e Some solutions for n=4 k=4
%e ..0..1..0..1. .0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..0..2
%e ..1..0..1..2. .1..0..2..0. .1..2..1..2. .1..2..1..0. .1..0..1..0
%e ..0..1..2..1. .0..1..0..2. .2..1..0..1. .2..1..0..1. .0..2..0..1
%e ..2..0..1..2. .2..0..2..0. .0..2..1..2. .1..0..1..0. .2..0..2..0
%Y Column 1 is A000079(n-2).
%Y Column 2 is A000244(n-1).
%Y Column 3 is A014445.
%Y Row 1 is A000079(n-2).
%Y Row 2 is A028859(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Jul 04 2016