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%I #4 Nov 27 2016 07:17:04
%S 0,6,6,40,152,40,155,1947,1947,155,456,17352,58904,17352,456,1128,
%T 121520,1410818,1410818,121520,1128,2472,712406,28637916,99992428,
%U 28637916,712406,2472,4950,3633649,506031118,6410559865,6410559865,506031118
%N T(n,k)=Number of nXk 0..3 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.
%C Table starts
%C .....0.........6.............40.................155......................456
%C .....6.......152...........1947...............17352...................121520
%C ....40......1947..........58904.............1410818.................28637916
%C ...155.....17352........1410818............99992428...............6410559865
%C ...456....121520.......28637916..........6410559865............1351385130108
%C ..1128....712406......506031118........374757577056..........268284486351027
%C ..2472...3633649.....7907770636......19983433877142........50067074390669892
%C ..4950..16547278...110655824716.....971720519011047......8732216738504713198
%C ..9240..68531079..1401584381570...43159978267689118...1415177080112634284232
%C .16302.261693631.16222274394016.1757375854436887414.212485358907612452321760
%H R. H. Hardin, <a href="/A278734/b278734.txt">Table of n, a(n) for n = 1..111</a>
%F Empirical for column k:
%F k=1: [polynomial of degree 7]
%F k=2: [polynomial of degree 28]
%F k=3: [polynomial of degree 109]
%e Some solutions for n=3 k=4
%e ..0..0..2..0. .0..0..3..1. .0..0..2..0. .1..0..2..1. .0..0..2..1
%e ..1..1..1..0. .1..0..1..1. .1..0..1..0. .1..1..2..1. .1..0..1..2
%e ..2..1..2..0. .1..1..3..0. .3..0..1..3. .2..3..0..1. .1..2..2..1
%Y Column 1 is A001919(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 27 2016