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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 00000101 or 00000111.
6

%I #4 Aug 28 2015 20:13:45

%S 48,76,76,172,134,172,338,270,270,338,628,462,468,462,628,1298,892,

%T 662,662,892,1298,2752,1751,1168,675,1168,1751,2752,5526,3299,2372,

%U 734,734,2372,3299,5526,10972,6324,3700,1443,676,1443,3700,6324,10972,22462

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000101 or 00000111.

%C Table starts

%C ....48....76...172..338..628.1298.2752.5526.10972.22462.46160.93354.188556

%C ....76...134...270..462..892.1751.3299.6324.12389.23874.46352.90232.175147

%C ...172...270...468..662.1168.2372.3700.6158.11812.19350.31112.58428..98160

%C ...338...462...662..675..734.1443.1416.1486..2556..3004..3232..4244...7152

%C ...628...892..1168..734..676.1818..984..748..1096..1168...880...958...2420

%C ..1298..1751..2372.1443.1818.4867.1294..748...968..1112...900..1504...4076

%C ..2752..3299..3700.1416..984.1294..744..632...812...874...656...764...1052

%C ..5526..6324..6158.1486..748..748..632..536...560...672...608...648....722

%C .10972.12389.11812.2556.1096..968..812..560...624...580...732...696....732

%C .22462.23874.19350.3004.1168.1112..874..672...580...628...702...654....668

%H R. H. Hardin, <a href="/A261709/b261709.txt">Table of n, a(n) for n = 1..3274</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 9] for n>11

%F k=2: [order 15] for n>17

%F k=3: [order 14] for n>20

%F k=4: a(n) = 3*a(n-7) +5*a(n-10) +a(n-13) -a(n-14) -a(n-17) -2*a(n-21) for n>27

%F k=5: a(n) = 2*a(n-7) -2*a(n-21) +a(n-28) for n>34

%F k=6: a(n) = a(n-14) for n>21

%F k=7: a(n) = a(n-14) for n>21

%F Empirical periodic continuations for column k:

%F k=6: period of length 14 starting at n=8: 748 968 1112 900 1504 4076 822 722 1018 1304 1188 1852 4804 1174

%F k=7: period of length 14 starting at n=8: 632 812 874 656 764 1052 600 540 692 824 688 780 1150 704

%F Empirical periodic continuations for diagonal:

%F diagonal: period of length 14 starting at n=8: 536 624 628 712 676 832 456 568 1036 704 616 696 2288 664

%F Empirical periodic tile pattern from columns 8-21 and rows 8-21:

%F ..536..560..672..608..648..722..660..552..602..728..596..552..620..612

%F ..560..624..580..732..696..732..686..604..830..856.1110..824..780..772

%F ..672..580..628..702..654..668..588..516..552..666..756..760..864..814

%F ..608..732..702..712..852..824..538..584..740..700..664..552..688..616

%F ..648..696..654..852..676.1000..640..780.1364..878..942..686.1010..704

%F ..722..732..668..824.1000..832..580..696..782..860.1112.1348.1560..932

%F ..660..686..588..538..640..580..456..568..566..538..570..656..678..560

%F ..552..604..516..584..780..696..568..568..646..572..572..684..594..520

%F ..602..830..552..740.1364..782..566..646.1036..828.1118.1492..830..652

%F ..728..856..666..700..878..860..538..572..828..704..754..984.1056..764

%F ..596.1110..756..664..942.1112..570..572.1118..754..616..642..976..648

%F ..552..824..760..552..686.1348..656..684.1492..984..642..696.1358..720

%F ..620..780..864..688.1010.1560..678..594..830.1056..976.1358.2288.1030

%F ..612..772..814..616..704..932..560..520..652..764..648..720.1030..664

%e Some solutions for n=7 k=4

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

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

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Aug 28 2015