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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 7

%I

%S 6,24,24,96,144,96,384,864,864,384,1536,5184,7776,5184,1536,6144,

%T 31104,69984,69984,31104,6144,24576,186624,629856,956448,629856,

%U 186624,24576,98304,1119744,5668704,13071456,13071456,5668704,1119744,98304,393216

%N 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 Table starts

%C .....6......24........96.........384..........1536............6144

%C ....24.....144.......864........5184.........31104..........186624

%C ....96.....864......7776.......69984........629856.........5668704

%C ...384....5184.....69984......956448......13071456.......178855776

%C ..1536...31104....629856....13071456.....271918944......5671161216

%C ..6144..186624...5668704...178855776....5671161216....180709558848

%C .24576.1119744..51018336..2447270496..118333620576...5764846339584

%C .98304.6718464.459165024.33489653472.2469841766784.184042295652096

%H R. H. Hardin, <a href="/A203984/b203984.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 6*4^(n-1)

%F k=2: a(n) = 4*6^n

%F k=3: a(n) = 96*9^(n-1)

%F k=4: a(n) = 15*a(n-1) -270*a(n-3) +324*a(n-4)

%F 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 k=6: (order 15 recurrence)

%F k=7: (order 45 recurrence)

%e Some solutions for n=4 k=3

%e ..0..0..0..0....0..0..0..0....0..0..1..1....0..1..0..0....0..1..2..1

%e ..1..1..1..2....1..2..1..2....1..2..2..0....2..2..2..1....2..1..2..0

%e ..0..0..0..2....1..2..1..0....0..0..1..1....0..0..0..0....2..0..2..1

%e ..1..1..1..1....0..2..1..2....1..2..2..0....1..1..1..1....1..1..2..1

%e ..0..2..2..2....1..2..1..2....1..0..1..1....2..2..2..2....2..0..0..1

%Y Column 1 is A002023(n-1)

%Y Column 2 is A067411(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 09 2012

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)