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A203826 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements 9

%I

%S 144,1296,1296,11664,27216,11664,104976,571536,571536,104976,944784,

%T 12002256,28005264,12002256,944784,8503056,252047376,1372257936,

%U 1372257936,252047376,8503056,76527504,5292994896,67240638864

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements

%C Table starts

%C .......144..........1296............11664...............104976

%C ......1296.........27216...........571536.............12002256

%C .....11664........571536.........28005264...........1372257936

%C ....104976......12002256.......1372257936.........157025515248

%C ....944784.....252047376......67240638864.......17968205387664

%C ...8503056....5292994896....3294791304336.....2056114528873776

%C ..76527504..111152892816..161444773912464...235282648691687184

%C .688747536.2334210749136.7910793921710736.26923572225438510384

%H R. H. Hardin, <a href="/A203826/b203826.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 16*9^n

%F k=2: a(n) = 1296*21^(n-1)

%F k=3: a(n) = 11664*49^(n-1)

%F k=4: a(n) = 117*a(n-1) -34398*a(n-3) +86436*a(n-4)

%F k=5: a(n) = 303*a(n-1) -8127*a(n-2) -394891*a(n-3) +4091304*a(n-4) +21176820*a(n-5) -92236816*a(n-6)

%F k=6: (order 16 recurrence)

%F k=7: (order 45 recurrence)

%e Some solutions for n=4 k=3

%e ..0..3..0..2....0..2..0..1....1..1..0..0....1..0..0..0....3..3..3..2

%e ..0..2..0..1....3..3..0..1....2..3..2..1....1..2..2..1....1..0..1..0

%e ..0..1..3..2....1..1..2..1....1..0..0..3....0..3..3..3....1..2..1..3

%e ..0..2..3..2....2..3..2..0....1..3..1..1....1..1..0..0....3..2..0..0

%e ..3..1..3..0....1..1..2..3....0..2..0..2....2..2..2..1....3..2..3..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 06 2012

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Last modified August 7 15:30 EDT 2020. Contains 336276 sequences. (Running on oeis4.)