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A233082 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

%I A233082 #6 Jul 23 2025 07:51:38
%S A233082 1,2,3,5,14,10,14,95,122,36,41,662,1985,1094,136,122,4631,32414,41675,
%T A233082 9842,528,365,32414,529862,1588262,875165,88574,2080,1094,226895,
%U A233082 8662343,60632429,77824814,18378455,797162,8256,3281,1588262,141615905
%N A233082 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
%C A233082 Table starts
%C A233082 ......1.........2.............5................14....................41
%C A233082 ......3........14............95...............662..................4631
%C A233082 .....10.......122..........1985.............32414................529862
%C A233082 .....36......1094.........41675...........1588262..............60632429
%C A233082 ....136......9842........875165..........77824814............6938214854
%C A233082 ....528.....88574......18378455........3813415862..........793945203881
%C A233082 ...2080....797162.....385947545......186857377214........90851753687090
%C A233082 ...8256...7174454....8104898435.....9156011483462.....10396235291448605
%C A233082 ..32896..64570082..170202867125...448644562689614...1189649113515482414
%C A233082 .131328.581130734.3574260209615.21983583571791062.136132453105625552657
%H A233082 R. H. Hardin, <a href="/A233082/b233082.txt">Table of n, a(n) for n = 1..241</a>
%F A233082 Empirical for column k:
%F A233082 k=1: a(n) = 6*a(n-1) -8*a(n-2)
%F A233082 k=2: a(n) = 10*a(n-1) -9*a(n-2)
%F A233082 k=3: a(n) = 22*a(n-1) -21*a(n-2)
%F A233082 k=4: a(n) = 50*a(n-1) -49*a(n-2)
%F A233082 k=5: a(n) = 118*a(n-1) -411*a(n-2) +294*a(n-3)
%F A233082 k=6: a(n) = 283*a(n-1) -4251*a(n-2) +13573*a(n-3) -9604*a(n-4)
%F A233082 k=7: [order 6]
%F A233082 Empirical for row n:
%F A233082 n=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A233082 n=2: a(n) = 8*a(n-1) -7*a(n-2) for n>3
%F A233082 n=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3) for n>5
%F A233082 n=4: a(n) = 49*a(n-1) -450*a(n-2) +1466*a(n-3) -1853*a(n-4) +789*a(n-5) for n>8
%F A233082 n=5: [order 10] for n>14
%F A233082 n=6: [order 21] for n>26
%F A233082 n=7: [order 52] for n>58
%e A233082 Some solutions for n=3 k=4
%e A233082 ..0..1..3..1....0..1..3..1....0..0..0..1....0..0..1..1....0..0..1..0
%e A233082 ..1..1..3..2....3..2..3..2....2..0..1..0....2..3..1..3....2..3..2..3
%e A233082 ..3..3..2..3....3..3..3..2....2..3..1..3....1..1..3..2....1..3..1..0
%Y A233082 Column 1 is A007582(n-1)
%Y A233082 Column 2 is A199560(n-1)
%Y A233082 Row 1 is A007051(n-1)
%K A233082 nonn,tabl
%O A233082 1,2
%A A233082 _R. H. Hardin_, Dec 03 2013