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A218319
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..2 nXk array
8
1, 3, 3, 7, 15, 7, 13, 63, 63, 13, 25, 249, 511, 249, 25, 49, 993, 4081, 4081, 993, 49, 97, 3969, 32641, 65089, 32641, 3969, 97, 191, 15867, 261121, 1040977, 1040977, 261121, 15867, 191, 375, 63423, 2088919, 16654561, 33296833, 16654561, 2088919, 63423
OFFSET
1,2
COMMENTS
Table starts
....1........3...........7..............13..................25
....3.......15..........63.............249.................993
....7.......63.........511............4081...............32641
...13......249........4081...........65089.............1040977
...25......993.......32641.........1040977............33296833
...49.....3969......261121........16654561..........1065434881
...97....15867.....2088919.......266461045.........34092332617
..191....63423....16710911......4263157633.......1090897313921
..375...253503...133683711.....68206942353......34906847699841
..737..1013265..1069441121...1091253912337....1116959510237537
.1449..4050081..8555300481..17459148261297...35740797133371201
.2849.16188417.68440576001.279331743809857.1143644481745733633
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)
k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5)
k=3: a(n) = 7*a(n-1) +7*a(n-2) +7*a(n-3) +7*a(n-4) +7*a(n-5)
k=4: a(n) = 14*a(n-1) +28*a(n-2) +55*a(n-3) +122*a(n-4) +292*a(n-5) -40*a(n-6) -66*a(n-7) -40*a(n-9) -118*a(n-10) +13*a(n-12) +13*a(n-15)
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
..1..0..0..0....0..0..0..0....1..1..0..1....0..0..1..1....1..0..1..0
..0..1..0..1....1..0..0..1....1..1..1..0....1..0..1..1....0..1..1..1
..0..0..0..0....1..1..0..1....0..0..0..0....0..0..1..0....0..0..0..1
CROSSREFS
Column 1 is A218199
Sequence in context: A060368 A218206 A218233 * A218196 A218372 A218242
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Oct 25 2012
STATUS
approved