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A214141 T(n,k)=Number of 0..4 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..4 introduced in row major order.

%I A214141 #6 Jul 22 2025 23:10:19
%S A214141 1,1,4,4,17,33,11,257,514,380,40,3074,28278,16388,4801,147,40434,
%T A214141 1101051,3221873,524296,62004,568,522515,47730973,396246659,367793014,
%U A214141 16777232,804833,2227,6800539,2000093424,56449101747,142612676441,41989913081
%N A214141 T(n,k)=Number of 0..4 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..4 introduced in row major order.
%C A214141 Table starts
%C A214141 ....1......1.........4...........11.............40...............147
%C A214141 ....4.....17.......257.........3074..........40434............522515
%C A214141 ...33....514.....28278......1101051.......47730973........2000093424
%C A214141 ..380..16388...3221873....396246659....56449101747.....7658621867351
%C A214141 .4801.524296.367793014.142612676441.66761857485037.29325981412599886
%H A214141 R. H. Hardin, <a href="/A214141/b214141.txt">Table of n, a(n) for n = 1..111</a>
%F A214141 Empirical for column k:
%F A214141 k=1: a(n) = 17*a(n-1) -55*a(n-2) +39*a(n-3)
%F A214141 k=2: a(n) = 34*a(n-1) -64*a(n-2)
%F A214141 k=3: a(n) = 129*a(n-1) -1759*a(n-2) +7575*a(n-3) -9064*a(n-4) +3120*a(n-5)
%F A214141 k=4: a(n) = 373*a(n-1) -4754*a(n-2) +15312*a(n-3)
%F A214141 k=5: (order 10)
%F A214141 k=6: (order 9)
%F A214141 Empirical for row n:
%F A214141 n=1: a(k)=6*a(k-1)-7*a(k-2)-6*a(k-3)+8*a(k-4)
%F A214141 n=2: a(k)=10*a(k-1)+50*a(k-2)-116*a(k-3)-361*a(k-4)+106*a(k-5)+312*a(k-6)
%F A214141 n=3: (order 15)
%F A214141 n=4: (order 37)
%e A214141 Some solutions for n=4 k=1
%e A214141 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A214141 ..2..3....1..2....1..2....1..0....2..3....1..0....2..3....1..0....2..3....2..0
%e A214141 ..3..2....2..0....2..3....2..1....0..4....2..3....3..2....2..3....1..4....0..1
%e A214141 ..4..0....3..4....1..0....1..2....1..0....0..4....2..0....3..4....4..3....1..3
%Y A214141 Column 1 is A198900
%K A214141 nonn,tabl
%O A214141 1,3
%A A214141 _R. H. Hardin_ Jul 05 2012