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%I #4 Mar 29 2013 20:31:29
%S 2,3,4,4,9,8,5,16,27,16,6,25,54,81,32,7,36,96,177,243,64,8,49,157,321,
%T 596,729,128,9,64,241,558,1062,2024,2187,256,10,81,352,928,1821,3645,
%U 6869,6561,512,11,100,494,1479,3115,5951,12856,23285,19683,1024,12,121
%N T(n,k)=Number of nXk 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing
%C Table starts
%C ....2.....3......4......5......6.......7.......8.......9......10......11
%C ....4.....9.....16.....25.....36......49......64......81.....100.....121
%C ....8....27.....54.....96....157.....241.....352.....494.....671.....887
%C ...16....81....177....321....558.....928....1479....2267....3356....4818
%C ...32...243....596...1062...1821....3115....5233....8564...13613...21017
%C ...64...729...2024...3645...5951....9919...16845...28558...47721...78071
%C ..128..2187...6869..12856..20275...31899...52532...89135..152495..259230
%C ..256..6561..23285..45626..71653..106838..166076..272997..464837..802560
%C ..512.19683..78942.161604.257568..372791..545443..849070.1401993.2401956
%C .1024.59049.267681.571202.928047.1333858.1866509.2733557.4294573.7150718
%H R. H. Hardin, <a href="/A223949/b223949.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical: columns k=1..7 have recurrences of order 1,1,5,10,16,24,33
%F Empirical: rows n=1..7 are polynomials of degree n for k>0,0,1,2,3,4,5
%e Some solutions for n=3 k=4
%e ..0..0..0..1....0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..0
%e ..0..0..1..1....0..1..1..1....0..1..1..1....0..0..0..0....0..0..0..1
%e ..0..0..1..1....0..1..1..1....0..0..0..0....0..0..0..1....0..1..1..1
%Y Column 1 is A000079
%Y Column 2 is A000244
%Y Row 1 is A000027(n+1)
%Y Row 2 is A000290(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 29 2013
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