%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