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A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.

%I A232335 #6 Jul 23 2025 07:19:22
%S A232335 1,2,1,4,6,1,6,18,16,1,10,32,74,42,1,16,82,154,308,110,1,26,162,628,
%T A232335 734,1282,288,1,42,388,1470,4906,3472,5338,754,1,68,806,5530,13170,
%U A232335 38986,16338,22228,1974,1,110,1858,13906,82526,117690,312276,76630,92562,5168
%N A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.
%C A232335 Table starts
%C A232335 .1.....2.......4.......6.........10.........16............26............42
%C A232335 .1.....6......18......32.........82........162...........388...........806
%C A232335 .1....16......74.....154........628.......1470..........5530.........13906
%C A232335 .1....42.....308.....734.......4906......13170.........82526........239992
%C A232335 .1...110....1282....3472......38986.....117690.......1274656.......4158066
%C A232335 .1...288....5338...16338.....312276....1047700......20052758......71916112
%C A232335 .1...754...22228...76630....2510674....9298730.....318521414....1241196022
%C A232335 .1..1974...92562..358656...20221026...82332898....5084744564...21383016966
%C A232335 .1..5168..385450.1676330..162993780..727588212...81376107850..367791626696
%C A232335 .1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234
%H A232335 R. H. Hardin, <a href="/A232335/b232335.txt">Table of n, a(n) for n = 1..448</a>
%F A232335 Empirical for column k:
%F A232335 k=1: a(n) = a(n-1)
%F A232335 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A232335 k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)
%F A232335 k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)
%F A232335 k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5
%F A232335 k=6: [order 7] for n>9
%F A232335 k=7: [order 16] for n>18
%F A232335 Empirical for row n:
%F A232335 n=1: a(n) = a(n-1) +a(n-2) for n>3
%F A232335 n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6
%F A232335 n=3: [order 8] for n>12
%F A232335 n=4: [order 21] for n>24
%F A232335 n=5: [order 36] for n>42
%F A232335 n=6: [order 80] for n>87
%e A232335 Some solutions for n=5 k=4
%e A232335 ..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1
%e A232335 ..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1
%e A232335 ..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2
%e A232335 ..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2
%e A232335 ..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..2
%Y A232335 Column 2 is A025169(n-1)
%Y A232335 Column 3 is A218059
%Y A232335 Row 1 is A006355(n+1)
%K A232335 nonn,tabl
%O A232335 1,2
%A A232335 _R. H. Hardin_, Nov 22 2013