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A203984 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

%I A203984 #7 Jul 22 2025 17:42:47
%S A203984 6,24,24,96,144,96,384,864,864,384,1536,5184,7776,5184,1536,6144,
%T A203984 31104,69984,69984,31104,6144,24576,186624,629856,956448,629856,
%U A203984 186624,24576,98304,1119744,5668704,13071456,13071456,5668704,1119744,98304,393216
%N A203984 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
%C A203984 Table starts
%C A203984 .....6......24........96.........384..........1536............6144
%C A203984 ....24.....144.......864........5184.........31104..........186624
%C A203984 ....96.....864......7776.......69984........629856.........5668704
%C A203984 ...384....5184.....69984......956448......13071456.......178855776
%C A203984 ..1536...31104....629856....13071456.....271918944......5671161216
%C A203984 ..6144..186624...5668704...178855776....5671161216....180709558848
%C A203984 .24576.1119744..51018336..2447270496..118333620576...5764846339584
%C A203984 .98304.6718464.459165024.33489653472.2469841766784.184042295652096
%H A203984 R. H. Hardin, <a href="/A203984/b203984.txt">Table of n, a(n) for n = 1..220</a>
%F A203984 Empirical for column k:
%F A203984 k=1: a(n) = 6*4^(n-1)
%F A203984 k=2: a(n) = 4*6^n
%F A203984 k=3: a(n) = 96*9^(n-1)
%F A203984 k=4: a(n) = 15*a(n-1) -270*a(n-3) +324*a(n-4)
%F A203984 k=5: a(n) = 25*a(n-1) -45*a(n-2) -963*a(n-3) +2025*a(n-4) +3645*a(n-5) -6561*a(n-6)
%F A203984 k=6: (order 15 recurrence)
%F A203984 k=7: (order 45 recurrence)
%e A203984 Some solutions for n=4 k=3
%e A203984 ..0..0..0..0....0..0..0..0....0..0..1..1....0..1..0..0....0..1..2..1
%e A203984 ..1..1..1..2....1..2..1..2....1..2..2..0....2..2..2..1....2..1..2..0
%e A203984 ..0..0..0..2....1..2..1..0....0..0..1..1....0..0..0..0....2..0..2..1
%e A203984 ..1..1..1..1....0..2..1..2....1..2..2..0....1..1..1..1....1..1..2..1
%e A203984 ..0..2..2..2....1..2..1..2....1..0..1..1....2..2..2..2....2..0..0..1
%Y A203984 Column 1 is A002023(n-1)
%Y A203984 Column 2 is A067411(n+1)
%K A203984 nonn,tabl
%O A203984 1,1
%A A203984 _R. H. Hardin_ Jan 09 2012