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A218242
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
8
1, 3, 3, 7, 15, 7, 15, 63, 63, 15, 29, 255, 511, 255, 29, 57, 1017, 4095, 4095, 1017, 57, 113, 4065, 32753, 65535, 32753, 4065, 113, 225, 16257, 262017, 1048545, 1048545, 262017, 16257, 225, 449, 65025, 2096129, 16776705, 33552513, 16776705, 2096129
OFFSET
1,2
COMMENTS
Table starts
....1........3...........7.............15...............29................57
....3.......15..........63............255.............1017..............4065
....7.......63.........511...........4095............32753............262017
...15......255........4095..........65535..........1048545..........16776705
...29.....1017.......32753........1048545.........33552513........1073678481
...57.....4065......262017.......16776705.......1073678481.......68715299265
..113....16257.....2096129......268427265......34357707105.....4397778640641
..225....65025....16769025.....4294836225....1099446617025...281457830657025
..449...260091...134152151....68717379375...35182291517157.18013301044272297
..895..1040319..1073216767..1099478066175.1125833320760065
.1783..4161087..8585730559.17591648997375
.3551.16643583.68685815807
LINKS
FORMULA
Empirical for column k:
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)
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)
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)
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)
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)
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
EXAMPLE
Some solutions for n=3 k=4
..0..0..1..1....1..0..0..0....1..1..0..0....0..1..1..1....1..0..1..0
..1..1..0..1....1..1..1..1....0..0..0..1....0..0..1..1....1..0..0..0
..1..0..1..0....0..0..1..1....1..1..0..0....1..0..1..1....0..0..0..1
CROSSREFS
Column 1 is A218189
Sequence in context: A218319 A218196 A218372 * A218288 A356976 A056420
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Oct 24 2012
STATUS
approved