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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
9

%I #6 Sep 17 2013 06:21:32

%S 1,3,3,7,15,7,13,59,59,13,25,233,483,233,25,49,929,3841,3841,929,49,

%T 97,3697,30599,61013,30599,3697,97,191,14719,243953,971849,971849,

%U 243953,14719,191,375,58599,1945103,15491481,30954777,15491481,1945103,58599

%N 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

%C Table starts

%C ....1........3...........7.............13...............25................49

%C ....3.......15..........59............233..............929..............3697

%C ....7.......59.........483...........3841............30599............243953

%C ...13......233........3841..........61013...........971849..........15491481

%C ...25......929.......30599.........971849.........30954777.........986715373

%C ...49.....3697......243953.......15491481........986715373.......62898202889

%C ...97....14719.....1945103......246985085......31459153095.....4010296932181

%C ..191....58599....15508803.....3937780585....1003007190421...255691410570153

%C ..375...233291...123654745....62780737565...31978263226027.16302319940388693

%C ..737...928769...985923281..1000923719573.1019542444050089

%C .1449..3697573..7860958915.15957894038581

%C .2849.14720617.62676962321

%H R. H. Hardin, <a href="/A218206/b218206.txt">Table of n, a(n) for n = 1..112</a>

%F 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

%e Some solutions for n=3 k=4

%e ..0..1..0..1....1..1..1..0....0..1..0..1....1..1..1..1....0..1..1..0

%e ..0..1..1..1....1..1..1..1....0..1..1..0....1..1..1..0....1..0..0..1

%e ..0..0..1..0....0..0..0..0....0..1..1..1....1..0..0..1....1..0..1..1

%Y Column 1 is A218199, see also A102026

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Oct 23 2012