A218319 - OEIS

%I #4 Oct 25 2012 17:12:57

%S 1,3,3,7,15,7,13,63,63,13,25,249,511,249,25,49,993,4081,4081,993,49,

%T 97,3969,32641,65089,32641,3969,97,191,15867,261121,1040977,1040977,

%U 261121,15867,191,375,63423,2088919,16654561,33296833,16654561,2088919,63423

%N T(n,k)=Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..2 nXk array

%C Table starts

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

%C ....3.......15..........63.............249.................993

%C ....7.......63.........511............4081...............32641

%C ...13......249........4081...........65089.............1040977

%C ...25......993.......32641.........1040977............33296833

%C ...49.....3969......261121........16654561..........1065434881

%C ...97....15867.....2088919.......266461045.........34092332617

%C ..191....63423....16710911......4263157633.......1090897313921

%C ..375...253503...133683711.....68206942353......34906847699841

%C ..737..1013265..1069441121...1091253912337....1116959510237537

%C .1449..4050081..8555300481..17459148261297...35740797133371201

%C .2849.16188417.68440576001.279331743809857.1143644481745733633

%H R. H. Hardin, <a href="/A218319/b218319.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5)

%F k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5)

%F k=3: a(n) = 7*a(n-1) +7*a(n-2) +7*a(n-3) +7*a(n-4) +7*a(n-5)

%F k=4: a(n) = 14*a(n-1) +28*a(n-2) +55*a(n-3) +122*a(n-4) +292*a(n-5) -40*a(n-6) -66*a(n-7) -40*a(n-9) -118*a(n-10) +13*a(n-12) +13*a(n-15)

%F Columns k=1..z+1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){(2^k-1)*a(n-i)} checked for z=1..3

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A218199

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Oct 25 2012