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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having its maximum diagonal element less than the absolute difference of its antidiagonal elements
8

%I #4 Dec 01 2014 20:02:16

%S 216,2920,2920,39594,137642,39594,536886,6505867,6505867,536886,

%T 7279536,307396791,1069722970,307396791,7279536,98701641,14522811996,

%U 175856353691,175856353691,14522811996,98701641,1338276196,686136478104

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having its maximum diagonal element less than the absolute difference of its antidiagonal elements

%C Table starts

%C .....216........2920..........39594............536886...............7279536

%C ....2920......137642........6505867.........307396791...........14522811996

%C ...39594.....6505867.....1069722970......175856353691........28911058486029

%C ..536886...307396791...175856353691...100642035373984.....57599526297754843

%C .7279536.14522811996.28911058486029.57599526297754843.114759773653630134486

%H R. H. Hardin, <a href="/A251359/b251359.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 7]

%F k=2: [order 27]

%F k=3: [order 96]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 01 2014