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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101
9

%I #4 Aug 01 2015 06:15:04

%S 48,82,82,188,131,188,364,288,288,364,644,496,700,496,644,1320,796,

%T 1224,1224,796,1320,2584,1645,1560,2235,1560,1645,2584,4842,2976,3470,

%U 2590,2590,3470,2976,4842,9412,4890,6908,6232,3828,6232,6908,4890,9412,18210

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101

%C Table starts

%C ....48....82...188...364....644...1320...2584...4842....9412...18210...35192

%C ....82...131...288...496....796...1645...2976...4890....9332...17659...30090

%C ...188...288...700..1224...1560...3470...6908..10070...18716...39478...64940

%C ...364...496..1224..2235...2590...6232..13170..17731...34192...77780..123488

%C ...644...796..1560..2590...3828...8646..16000..24508...49816..103124..168848

%C ..1320..1645..3470..6232...8646..19718..37882..58489..116930..248515..412314

%C ..2584..2976..6908.13170..16000..37882..80516.119194..231008..526102..890868

%C ..4842..4890.10070.17731..24508..58489.119194.181176..369672..835045.1415774

%C ..9412..9332.18716.34192..49816.116930.231008.369672..766388.1697970.2896836

%C .18210.17659.39478.77780.103124.248515.526102.835045.1697970.3885356.6805170

%H R. H. Hardin, <a href="/A260841/b260841.txt">Table of n, a(n) for n = 1..612</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 14] for n>15

%F k=2: [order 18] for n>19

%F k=3: [order 22] for n>24

%F k=4: [order 33] for n>34

%F k=5: [order 59] for n>63

%F k=6: [order 92] for n>96

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Aug 01 2015