A218288 T(n,k)=Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..4 nXk array.

1, 3, 3, 7, 15, 7, 15, 63, 63, 15, 31, 255, 511, 255, 31, 61, 1019, 4091, 4091, 1019, 61, 121, 4073, 32739, 65507, 32739, 4073, 121, 241, 16289, 261905, 1048307, 1048307, 261905, 16289, 241, 481, 65153, 2095233, 16772877, 33549827, 16772877, 2095233

Offset

1,2

Comments

Table starts

....1........3..........7............15.............31..............61

....3.......15.........63...........255...........1019............4073

....7.......63........511..........4091..........32739..........261905

...15......255.......4091.........65507........1048307........16772877

...31.....1019......32739.......1048307.......33549827......1073597617

...61.....4073.....261905......16772877.....1073597617.....68710447465

..121....16289....2095233.....268366049....34355128651...4397469258389

..241....65153...16761837....4293856057..1099364046509.281438014358653

..481...260609..134094563...68701687597.35179647135791

..961..1042417.1072755573.1099226869621

.1921..4169595.8582037499

.3839.16678079

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical: Column k=1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){a(n-i)} z=1,2,3,4

Example

Some solutions for n=3 k=4
..0..1..1..1....1..0..0..1....1..0..0..0....0..0..0..0....0..1..1..0
..1..1..0..1....0..1..0..1....1..0..0..1....1..1..0..1....0..0..1..1
..0..1..1..1....0..1..0..1....1..1..0..0....1..1..1..0....1..0..0..0

Crossrefs

Sequence in context: A218196 A218372 A218242 * A356976 A056420 A030069

Adjacent sequences: A218285 A218286 A218287 * A218289 A218290 A218291

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 25 2012

Status

approved