A218196 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..3 nXk array.

1, 3, 3, 7, 15, 7, 15, 63, 63, 15, 29, 251, 507, 251, 29, 57, 1001, 4067, 4067, 1001, 57, 113, 4001, 32529, 65251, 32529, 4001, 113, 225, 16001, 260205, 1044001, 1044001, 260205, 16001, 225, 449, 63985, 2081511, 16703113, 33407143, 16703113, 2081511

Offset

1,2

Comments

Table starts

....1........3...........7.............15...............29................57

....3.......15..........63............251.............1001..............4001

....7.......63.........507...........4067............32529............260205

...15......251........4067..........65251..........1044001..........16703113

...29.....1001.......32529........1044001.........33407143........1068969245

...57.....4001......260205.......16703113.......1068969245.......68410191725

..113....16001.....2081511......267240217......34205771911.....4378092248621

..225....63985....16651157.....4275711525....1094550718437...280189181606213

..449...255867...133202247....68409381991...35024601762415.17931584186079329

..895..1023171..1065561647..1094518209251.1120754736783429

.1783..4091495..8524042607.17511781134639

.3551.16361227.68188735807

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

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
..1..1..1..1....0..1..1..0....1..0..0..1....0..1..1..0....1..0..0..1
..1..0..1..0....1..0..0..0....0..1..0..0....1..0..1..0....1..1..0..1
..0..1..1..0....0..1..1..0....1..0..1..0....0..0..0..0....1..0..0..1

Crossrefs

Sequence in context: A218206 A218233 A218319 * A218372 A218242 A218288

Adjacent sequences: A218193 A218194 A218195 * A218197 A218198 A218199

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 23 2012

Status

approved