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 A214166 T(n,k)=Number of 0..5 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..5 introduced in row major order 14

%I #4 Jul 05 2012 21:32:28

%S 1,1,4,4,18,34,11,337,902,481,41,5994,88261,60320,8731,161,121778,

%T 7386816,27240856,4242606,174454,694,2518082,655418810,9601970064,

%U 8548472292,300785428,3603244,3151,52655411,57661437162,3598372134742

%N T(n,k)=Number of 0..5 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..5 introduced in row major order

%C Table starts

%C ....1.......1..........4.............11................41..................161

%C ....4......18........337...........5994............121778..............2518082

%C ...34.....902......88261........7386816.........655418810..........57661437162

%C ..481...60320...27240856.....9601970064.....3598372134742.....1329144373535118

%C .8731.4242606.8548472292.12515731371696.19767477649307133.30641183868207736684

%H R. H. Hardin, <a href="/A214166/b214166.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical for column k:

%F k=1: a(n) = 32*a(n-1) -262*a(n-2) +672*a(n-3) -441*a(n-4)

%F k=2: a(n) = 84*a(n-1) -945*a(n-2) +1562*a(n-3)

%F k=3: a(n) = 370*a(n-1) -18411*a(n-2) +297448*a(n-3) -1839799*a(n-4) +4424682*a(n-5) -4113757*a(n-6) +1249468*a(n-7)

%F k=4: a(n) = 1402*a(n-1) -130492*a(n-2) +2979072*a(n-3) -15573492*a(n-4) +12571416*a(n-5)

%F k=5: (order 15)

%F Empirical for row n:

%F n=1: a(k)=10*a(k-1)-30*a(k-2)+20*a(k-3)+31*a(k-4)-30*a(k-5)

%F n=2: a(k)=21*a(k-1)+49*a(k-2)-959*a(k-3)-1869*a(k-4)+7679*a(k-5)+15051*a(k-6)-6741*a(k-7)-13230*a(k-8)

%F n=3: (order 22)

%F n=4: (order 60)

%e Some solutions for n=4 k=1

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

%e ..1..2....1..2....1..2....1..2....1..2....1..0....1..0....1..0....2..3....2..3

%e ..3..4....0..1....3..0....2..0....0..3....2..1....2..3....2..3....3..1....0..1

%e ..5..3....1..0....0..4....0..2....1..2....0..2....0..4....1..0....4..2....1..3

%Y Column 1 is A198900

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Jul 05 2012

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)