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%I #4 Jan 29 2014 07:23:29
%S 256,2596,2596,25950,55000,25950,256376,1110784,1110784,256376,
%T 2525698,21573924,44087440,21573924,2525698,24922062,415734304,
%U 1595240268,1595240268,415734304,24922062,246386369,8222889690,59688228619
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays colored with the maximum plus the upper median of every 2X2 subblock
%C Table starts
%C .........256..........2596..........25950..........256376..........2525698
%C ........2596.........55000........1110784........21573924........415734304
%C .......25950.......1110784.......44087440......1595240268......59688228619
%C ......256376......21573924.....1595240268....114361325908....8637812725732
%C .....2525698.....415734304....59688228619...8637812725732.1368429194765626
%C ....24922062....8222889690..2315388775024.686154548079428
%C ...246386369..162119665374.89774785525354
%C ..2433171504.3173047388586
%C .24010605844
%H R. H. Hardin, <a href="/A236601/b236601.txt">Table of n, a(n) for n = 1..49</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 20] for n>22
%e Some solutions for n=2 k=4
%e ..0..0..3..0..1....0..1..3..0..2....1..0..0..0..0....0..0..2..0..0
%e ..1..0..0..2..1....1..0..2..3..0....1..0..0..1..3....0..0..0..3..0
%e ..0..2..0..2..3....0..2..1..0..1....0..3..2..2..0....1..0..0..1..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 29 2014