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

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

R. H. Hardin, Table of n, a(n) for n = 1..144

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

Adjacent sequences: A218316 A218317 A218318 * A218320 A218321 A218322

Keyword

nonn,tabl

Author

R. H. Hardin Oct 25 2012

Status

approved