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A274749 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.

%I A274749 #4 Jul 04 2016 10:19:04
%S A274749 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 A274749 610,243,32,64,448,2017,4554,4967,2584,729,64,128,1224,7858,25585,
%U A274749 40242,30349,10946,2187,128,256,3344,30605,143634,327123,355504,185435,46368
%N A274749 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 A274749 Table starts
%C A274749 ...1.....1......2........4..........8...........16............32
%C A274749 ...1.....3......8.......22.........60..........164...........448
%C A274749 ...2.....9.....34......133........518.........2017..........7858
%C A274749 ...4....27....144......813.......4554........25585........143634
%C A274749 ...8....81....610.....4967......40242.......327123.......2661918
%C A274749 ..16...243...2584....30349.....355504......4190533......49475642
%C A274749 ..32...729..10946...185435....3140840.....53680592.....920432562
%C A274749 ..64..2187..46368..1133025...27748676....687685512...17123659885
%C A274749 .128..6561.196418..6922887..245154340...8809672678..318581114142
%C A274749 .256.19683.832040.42299477.2165891856.112857546696.5927090659144
%H A274749 R. H. Hardin, <a href="/A274749/b274749.txt">Table of n, a(n) for n = 1..363</a>
%F A274749 Empirical for column k:
%F A274749 k=1: a(n) = 2*a(n-1) for n>2
%F A274749 k=2: a(n) = 3*a(n-1)
%F A274749 k=3: a(n) = 4*a(n-1) +a(n-2)
%F A274749 k=4: a(n) = 6*a(n-1) +a(n-2) -2*a(n-3) for n>4
%F A274749 k=5: a(n) = 9*a(n-1) -14*a(n-3) +10*a(n-4) -2*a(n-5) for n>6
%F A274749 k=6: [order 9] for n>11
%F A274749 k=7: [order 13] for n>15
%F A274749 Empirical for row n:
%F A274749 n=1: a(n) = 2*a(n-1) for n>2
%F A274749 n=2: a(n) = 2*a(n-1) +2*a(n-2)
%F A274749 n=3: a(n) = 2*a(n-1) +7*a(n-2) +2*a(n-3) -2*a(n-4)
%F A274749 n=4: [order 8]
%F A274749 n=5: [order 16] for n>17
%F A274749 n=6: [order 36] for n>38
%F A274749 n=7: [order 80] for n>83
%e A274749 Some solutions for n=4 k=4
%e A274749 ..0..1..0..1. .0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..0..2
%e A274749 ..1..0..1..2. .1..0..2..0. .1..2..1..2. .1..2..1..0. .1..0..1..0
%e A274749 ..0..1..2..1. .0..1..0..2. .2..1..0..1. .2..1..0..1. .0..2..0..1
%e A274749 ..2..0..1..2. .2..0..2..0. .0..2..1..2. .1..0..1..0. .2..0..2..0
%Y A274749 Column 1 is A000079(n-2).
%Y A274749 Column 2 is A000244(n-1).
%Y A274749 Column 3 is A014445.
%Y A274749 Row 1 is A000079(n-2).
%Y A274749 Row 2 is A028859(n-1).
%K A274749 nonn,tabl
%O A274749 1,4
%A A274749 _R. H. Hardin_, Jul 04 2016