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%I #4 Dec 29 2014 09:08:53
%S 16,47,47,125,132,125,335,306,306,335,907,742,494,742,907,2470,1775,
%T 914,914,1775,2470,6740,4158,1709,1498,1709,4158,6740,18406,9551,3241,
%U 2543,2543,3241,9551,18406,50278,21591,6231,4490,3936,4490,6231,21591,50278
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically
%C Table starts
%C .....16.....47...125...335...907..2470...6740..18406..50278.137354.375250
%C .....47....132...306...742..1775..4158...9551..21591..48179.106371.232787
%C ....125....306...494...914..1709..3241...6231..12122..23800..47037..93377
%C ....335....742...914..1498..2543..4490...8216..15476..29780..58148.114620
%C ....907...1775..1709..2543..3936..6414..11022..19851..37083..71082.138576
%C ...2470...4158..3241..4490..6414..9630..15363..26064..46635..86880.166407
%C ...6740...9551..6231..8216.11022.15363..22656..35736..60273.107607.200418
%C ..18406..21591.12122.15476.19851.26064..35736..52110..81672.137394.245220
%C ..50278..48179.23800.29780.37083.46635..60273..81672.118182.184503.310035
%C .137354.106371.47037.58148.71082.86880.107607.137394.184503.265458.413307
%H R. H. Hardin, <a href="/A253231/b253231.txt">Table of n, a(n) for n = 1..833</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -2*a(n-3) for n>6
%F k=2: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>7
%F k=3..7: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4) for n>8
%e Some solutions for n=4 k=4
%e ..0..0..0..0..1....0..1..0..0..1....0..1..1..1..1....0..0..1..1..1
%e ..1..0..0..0..0....0..1..0..0..0....0..1..1..1..1....0..0..0..0..0
%e ..1..0..0..0..0....0..1..0..0..0....1..1..1..1..1....1..1..0..0..0
%e ..1..0..0..0..0....1..1..0..0..0....0..0..0..0..0....1..1..0..0..0
%e ..1..0..0..1..1....1..1..0..0..0....0..0..0..0..1....1..0..0..1..1
%Y Column 1 is A204609
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 29 2014
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