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%I #4 Jan 11 2014 17:48:17
%S 81,498,498,2996,6954,2996,15782,102687,102687,15782,80584,1241251,
%T 4295649,1241251,80584,388008,14564613,140614400,140614400,14564613,
%U 388008,1819537,152335168,4492923265,13038576512,4492923265,152335168
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock two median terms lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C ........81..........498...........2996............15782.............80584
%C .......498.........6954.........102687..........1241251..........14564613
%C ......2996.......102687........4295649........140614400........4492923265
%C .....15782......1241251......140614400......13038576512.....1209080327197
%C .....80584.....14564613.....4492923265....1209080327197...335281754960247
%C ....388008....152335168...120808065816...92361300067563.76271328945497498
%C ...1819537...1529460228..3063485786072.6600170210621221
%C ...8271237..14358083795.69645586587955
%C ..36871545.129965217502
%C .161304512
%H R. H. Hardin, <a href="/A235531/b235531.txt">Table of n, a(n) for n = 1..59</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 17]
%e Some solutions for n=2 k=4
%e ..0..0..1..1..1....0..0..0..2..2....0..0..0..2..2....1..0..0..1..0
%e ..0..0..0..0..0....0..0..2..0..2....0..0..1..0..2....0..0..0..2..2
%e ..0..1..2..0..0....2..1..1..0..1....1..2..1..0..1....1..1..1..0..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
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