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%I #4 Dec 03 2012 09:09:02
%S 2,2,3,3,4,4,4,6,6,5,5,9,10,8,6,6,12,19,15,10,7,7,15,30,34,21,12,8,8,
%T 18,42,61,55,28,14,9,9,21,55,95,111,83,36,16,10,10,24,69,137,192,187,
%U 119,45,18,11,11,27,84,187,302,358,297,164,55,20,12,12,30,100,246,442,613,626
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 nXk array
%C Table starts
%C ..2..2..3...4....5....6.....7.....8.....9....10....11....12....13....14...15
%C ..3..4..6...9...12...15....18....21....24....27....30....33....36....39...42
%C ..4..6.10..19...30...42....55....69....84...100...117...135...154...174..195
%C ..5..8.15..34...61...95...137...187...246...315...395...487...592...711..845
%C ..6.10.21..55..111..192...302...442...618...838..1111..1447..1857..2353.2948
%C ..7.12.28..83..187..358...613...962..1426..2034..2823..3839..5137..6782.8850
%C ..8.14.36.119..297..626..1165..1963..3088..4630..6711..9492.13175.18010
%C ..9.16.45.164..450.1038..2094..3789..6334..9995.15133.22239.31956
%C .10.18.55.219..656.1646..3587..6962.12375.20581.32588
%C .11.20.66.285..926.2513..5893.12243.23132.40583
%C .12.22.78.363.1272.3714..9335.20705.41537
%C .13.24.91.454.1707.5337.14323.33819
%H R. H. Hardin, <a href="/A220032/b220032.txt">Table of n, a(n) for n = 1..198</a>
%e Some solutions for n=3 k=4
%e ..0..0..0..0....1..0..0..0....1..0..0..0....0..0..0..0....1..0..0..0
%e ..0..0..0..0....1..1..0..0....1..0..0..0....1..1..0..0....1..1..1..0
%e ..1..1..0..0....1..1..0..0....1..0..0..0....1..1..1..1....1..1..1..1
%Y Column 1 is A000027(n+1)
%Y Column 2 is A004275(n+1)
%Y Column 3 is A000217(n+1)
%Y Column 4 is A062748 for n>1
%Y Row 1 is A000027
%Y Row 2 is A204502(n+3)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 03 2012
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