login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 20:02 EST 2022. Contains 350599 sequences. (Running on oeis4.)