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 A218319 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 8
 1, 3, 3, 7, 15, 7, 13, 63, 63, 13, 25, 249, 511, 249, 25, 49, 993, 4081, 4081, 993, 49, 97, 3969, 32641, 65089, 32641, 3969, 97, 191, 15867, 261121, 1040977, 1040977, 261121, 15867, 191, 375, 63423, 2088919, 16654561, 33296833, 16654561, 2088919, 63423 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ....1........3...........7..............13..................25 ....3.......15..........63.............249.................993 ....7.......63.........511............4081...............32641 ...13......249........4081...........65089.............1040977 ...25......993.......32641.........1040977............33296833 ...49.....3969......261121........16654561..........1065434881 ...97....15867.....2088919.......266461045.........34092332617 ..191....63423....16710911......4263157633.......1090897313921 ..375...253503...133683711.....68206942353......34906847699841 ..737..1013265..1069441121...1091253912337....1116959510237537 .1449..4050081..8555300481..17459148261297...35740797133371201 .2849.16188417.68440576001.279331743809857.1143644481745733633 LINKS R. H. Hardin, Table of n, a(n) for n = 1..144 FORMULA Empirical for column k: k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5) k=3: a(n) = 7*a(n-1) +7*a(n-2) +7*a(n-3) +7*a(n-4) +7*a(n-5) 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) 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 EXAMPLE Some solutions for n=3 k=4 ..1..0..0..0....0..0..0..0....1..1..0..1....0..0..1..1....1..0..1..0 ..0..1..0..1....1..0..0..1....1..1..1..0....1..0..1..1....0..1..1..1 ..0..0..0..0....1..1..0..1....0..0..0..0....0..0..1..0....0..0..0..1 CROSSREFS Column 1 is A218199 Sequence in context: A060368 A218206 A218233 * A218196 A218372 A218242 Adjacent sequences:  A218316 A218317 A218318 * A218320 A218321 A218322 KEYWORD nonn,tabl AUTHOR R. H. Hardin Oct 25 2012 STATUS approved

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Last modified January 26 20:02 EST 2022. Contains 350599 sequences. (Running on oeis4.)