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A229320 T(n,k)=Number of nXk 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..3 array without adjacent equal elements in the latter.

%I A229320 #6 Jul 23 2025 05:40:41
%S A229320 4,14,14,50,154,50,176,1494,1494,176,622,13968,34022,13968,622,2196,
%T A229320 129766,717882,717882,129766,2196,7756,1203222,14972226,33330044,
%U A229320 14972226,1203222,7756,27390,11146054,310664552,1520769276,1520769276
%N A229320 T(n,k)=Number of nXk 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..3 array without adjacent equal elements in the latter.
%C A229320 Table starts
%C A229320 .....4........14...........50.............176..............622.............2196
%C A229320 ....14.......154.........1494...........13968...........129766..........1203222
%C A229320 ....50......1494........34022..........717882.........14972226........310664552
%C A229320 ...176.....13968.......717882........33330044.......1520769276......69027667944
%C A229320 ...622....129766.....14972226......1520769276.....151503568022...14999158146398
%C A229320 ..2196...1203222....310664552.....69027667944...14999158146398.3239971166331308
%C A229320 ..7756..11146054...6441333794...3129534386120.1483911991489430
%C A229320 .27390.103236194.133479301256.141829123448362
%H A229320 R. H. Hardin, <a href="/A229320/b229320.txt">Table of n, a(n) for n = 1..71</a>
%F A229320 Empirical for column k:
%F A229320 k=1: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +2*a(n-4)
%F A229320 k=2: [order 65]
%e A229320 Some solutions for n=2 k=4
%e A229320 ..3..1..3..0....1..2..3..2....1..2..2..2....1..2..2..0....2..0..1..0
%e A229320 ..2..1..2..3....0..3..0..3....2..2..1..2....0..1..0..3....1..2..1..1
%K A229320 nonn,tabl
%O A229320 1,1
%A A229320 _R. H. Hardin_ Sep 19 2013