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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 00010011
9

%I #4 Jul 30 2015 22:50:42

%S 48,82,82,190,115,190,350,265,265,350,622,481,652,481,622,1315,798,

%T 1234,1234,798,1315,2478,1671,1740,2449,1740,1671,2478,4597,3196,3891,

%U 3328,3328,3891,3196,4597,9184,5596,8056,7645,5256,7645,8056,5596,9184,17591

%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 00010011

%C Table starts

%C ....48....82...190....350....622...1315...2478....4597....9184...17591....33096

%C ....82...115...265....481....798...1671...3196....5596...11008...21414....38685

%C ...190...265...652...1234...1740...3891...8056...12829...24824...52425....91422

%C ...350...481..1234...2449...3328...7645..16095...25501...51049..109299...189890

%C ...622...798..1740...3328...5256..11107..21594...38145...75910..151311...277024

%C ..1315..1671..3891...7645..11107..24103..48788...83655..166775..348791...629945

%C ..2478..3196..8056..16095..21594..48788.104308..173103..341748..744619..1358260

%C ..4597..5596.12829..25501..38145..83655.173103..305402..619749.1314687..2454814

%C ..9184.11008.24824..51049..75910.166775.341748..619749.1256376.2669676..5022096

%C .17591.21414.52425.109299.151311.348791.744619.1314687.2669676.5925416.11179072

%H R. H. Hardin, <a href="/A260767/b260767.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 20] for n>23

%F k=3: [order 32] for n>34

%F k=4: [order 52] for n>58

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 30 2015