login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


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

R. H. Hardin, Table of n, a(n) for n = 1..112

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 A056420 A030069

Adjacent sequences:  A218239 A218240 A218241 * A218243 A218244 A218245

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Oct 24 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 March 4 02:31 EST 2021. Contains 341773 sequences. (Running on oeis4.)