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A229372 T(n,k)=Number of nXk 0..2 arrays avoiding 11 horizontally, 22 vertically and 00 antidiagonally.

%I A229372 #6 Jul 23 2025 05:41:30
%S A229372 3,8,8,22,38,22,60,184,184,60,164,869,1610,869,164,448,4144,13937,
%T A229372 13937,4144,448,1224,19675,122497,222990,122497,19675,1224,3344,93589,
%U A229372 1067299,3576912,3576912,1067299,93589,3344,9136,444824,9346997,56939585
%N A229372 T(n,k)=Number of nXk 0..2 arrays avoiding 11 horizontally, 22 vertically and 00 antidiagonally.
%C A229372 Table starts
%C A229372 ....3......8.......22..........60...........164.............448
%C A229372 ....8.....38......184.........869..........4144...........19675
%C A229372 ...22....184.....1610.......13937........122497.........1067299
%C A229372 ...60....869....13937......222990.......3576912........56939585
%C A229372 ..164...4144...122497.....3576912.....104382552......3043629267
%C A229372 ..448..19675..1067299....56939585....3043629267....162794962814
%C A229372 .1224..93589..9346997...911301584...89084628843...8710922742428
%C A229372 .3344.444824.81633583.14532090528.2599351293506.465220677212678
%H A229372 R. H. Hardin, <a href="/A229372/b229372.txt">Table of n, a(n) for n = 1..364</a>
%F A229372 Empirical for column k:
%F A229372 k=1: a(n) = 2*a(n-1) +2*a(n-2)
%F A229372 k=2: a(n) = 2*a(n-1) +13*a(n-2) +3*a(n-3) -13*a(n-4) +4*a(n-5)
%F A229372 k=3: [order 11]
%F A229372 k=4: [order 24] for n>25
%F A229372 k=5: [order 50] for n>54
%e A229372 Some solutions for n=3 k=4
%e A229372 ..2..1..2..2....1..2..0..2....0..1..0..0....1..0..2..1....0..1..0..1
%e A229372 ..0..2..1..0....0..1..2..1....1..2..2..2....2..1..0..0....2..1..0..2
%e A229372 ..2..0..1..2....2..1..0..1....0..0..0..1....1..2..1..2....1..2..2..1
%Y A229372 Column 1 is A028859
%K A229372 nonn,tabl
%O A229372 1,1
%A A229372 _R. H. Hardin_ Sep 21 2013