A218206 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..2 nXk array

1, 3, 3, 7, 15, 7, 13, 59, 59, 13, 25, 233, 483, 233, 25, 49, 929, 3841, 3841, 929, 49, 97, 3697, 30599, 61013, 30599, 3697, 97, 191, 14719, 243953, 971849, 971849, 243953, 14719, 191, 375, 58599, 1945103, 15491481, 30954777, 15491481, 1945103, 58599

Offset

1,2

Comments

Table starts

....1........3...........7.............13...............25................49

....3.......15..........59............233..............929..............3697

....7.......59.........483...........3841............30599............243953

...13......233........3841..........61013...........971849..........15491481

...25......929.......30599.........971849.........30954777.........986715373

...49.....3697......243953.......15491481........986715373.......62898202889

...97....14719.....1945103......246985085......31459153095.....4010296932181

..191....58599....15508803.....3937780585....1003007190421...255691410570153

..375...233291...123654745....62780737565...31978263226027.16302319940388693

..737...928769...985923281..1000923719573.1019542444050089

.1449..3697573..7860958915.15957894038581

.2849.14720617.62676962321

Links

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

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

Crossrefs

Column 1 is A218199, see also A102026

Sequence in context: A049772 A119470 A060368 * A218233 A218319 A218196

Adjacent sequences: A218203 A218204 A218205 * A218207 A218208 A218209

Keyword

nonn,tabl

Author

R. H. Hardin Oct 23 2012

Status

approved