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%I #4 Oct 24 2012 08:30:47
%S 1,3,3,7,15,7,15,63,63,15,29,255,511,255,29,57,1017,4095,4095,1017,57,
%T 113,4065,32753,65535,32753,4065,113,225,16257,262017,1048545,1048545,
%U 262017,16257,225,449,65025,2096129,16776705,33552513,16776705,2096129
%N T(n,k)=Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..3 nXk array
%C Table starts
%C ....1........3...........7.............15...............29................57
%C ....3.......15..........63............255.............1017..............4065
%C ....7.......63.........511...........4095............32753............262017
%C ...15......255........4095..........65535..........1048545..........16776705
%C ...29.....1017.......32753........1048545.........33552513........1073678481
%C ...57.....4065......262017.......16776705.......1073678481.......68715299265
%C ..113....16257.....2096129......268427265......34357707105.....4397778640641
%C ..225....65025....16769025.....4294836225....1099446617025...281457830657025
%C ..449...260091...134152151....68717379375...35182291517157.18013301044272297
%C ..895..1040319..1073216767..1099478066175.1125833320760065
%C .1783..4161087..8585730559.17591648997375
%C .3551.16643583.68685815807
%H R. H. Hardin, <a href="/A218242/b218242.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7)
%F k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) +3*a(n-7)
%F k=3: a(n) = 7*a(n-1) +7*a(n-2) +7*a(n-3) +7*a(n-4) +7*a(n-5) +7*a(n-6) +7*a(n-7)
%F k=4: a(n) = 15*a(n-1) +15*a(n-2) +15*a(n-3) +15*a(n-4) +15*a(n-5) +15*a(n-6) +15*a(n-7)
%F k=5: a(n) = 30*a(n-1) +60*a(n-2) +120*a(n-3) +239*a(n-4) +506*a(n-5) +1124*a(n-6) +2696*a(n-7) -207*a(n-8) -412*a(n-9) -644*a(n-10) -207*a(n-12) -764*a(n-13) -1692*a(n-14) +117*a(n-16) +262*a(n-17) +117*a(n-20) +378*a(n-21) -29*a(n-24) -29*a(n-28)
%F Columns k=1..z+1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){(2^k-1)*a(n-i)} checked for z=1..3
%e Some solutions for n=3 k=4
%e ..0..0..1..1....1..0..0..0....1..1..0..0....0..1..1..1....1..0..1..0
%e ..1..1..0..1....1..1..1..1....0..0..0..1....0..0..1..1....1..0..0..0
%e ..1..0..1..0....0..0..1..1....1..1..0..0....1..0..1..1....0..0..0..1
%Y Column 1 is A218189
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Oct 24 2012