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A261553 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000101 or 00001011. 6

%I #4 Aug 24 2015 11:02:29

%S 48,80,80,170,132,170,336,269,269,336,652,484,516,484,652,1293,871,

%T 754,754,871,1293,2588,1702,1210,769,1210,1702,2588,5100,3230,2187,

%U 816,816,2187,3230,5100,9996,6084,3436,1286,656,1286,3436,6084,9996,19788,11656

%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 00001011.

%C Table starts

%C ....48....80...170..336..652.1293.2588.5100..9996.19788.39102.76977.151492

%C ....80...132...269..484..871.1702.3230.6084.11656.22140.41998.80163.152575

%C ...170...269...516..754.1210.2187.3436.5368..9414.14902.22538.38820..62948

%C ...336...484...754..769..816.1286.1510.1615..2362..3215..3431..4393...7048

%C ...652...871..1210..816..656.1273.1084..855..1036..1259...906...967...1868

%C ..1293..1702..2187.1286.1273.2879.1566..857...828..1130...786...961...2211

%C ..2588..3230..3436.1510.1084.1566..824..602...738..1065...640...756...1266

%C ..5100..6084..5368.1615..855..857..602..502...626...904...634...685....822

%C ..9996.11656..9414.2362.1036..828..738..626...668...690...656...603....634

%C .19788.22140.14902.3215.1259.1130.1065..904...690...612...640...677....665

%H R. H. Hardin, <a href="/A261553/b261553.txt">Table of n, a(n) for n = 1..3609</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 12] for n>14

%F k=2: [order 16] for n>17

%F k=3: [order 23] for n>30

%F k=4: [order 38] for n>44

%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>23

%F k=7: a(n) = a(n-14) for n>23

%F Empirical apparent periods for column k:

%F k=6: period of length 14 starting at n=10: 1130 786 961 2211 1036 680 881 1315 1001 1173 2670 1430 806 822

%F k=7: period of length 14 starting at n=10: 1065 640 756 1266 641 502 648 1022 654 782 1353 740 578 734

%F Empirical apparent period for diagonal:

%F diagonal: period of length 14 starting at n=10: 612 648 724 688 458 512 800 688 608 556 1606 656 478 652

%F Empirical repeating tile pattern from columns 10-23 and rows 10-23:

%F ..612..640..677..665..565..495..547..650..709..729..798..821..768..666

%F ..640..648..819..804..545..528..591..668..628..528..606..574..610..652

%F ..677..819..724..820..585..662..831..866..893..640..732..652..653..599

%F ..665..804..820..688..532..620..687..850.1019.1032.1147..926..746..628

%F ..565..545..585..532..458..516..512..522..559..611..619..557..592..598

%F ..495..528..662..620..516..512..577..518..512..584..527..460..495..560

%F ..547..591..831..687..512..577..800..777..929..958..735..574..601..726

%F ..650..668..866..850..522..518..777..688..737..918..983..778..791..896

%F ..709..628..893.1019..559..512..929..737..608..602..821..588..594..990

%F ..729..528..640.1032..611..584..958..918..602..556..944..678..575..726

%F ..798..606..732.1147..619..527..735..983..821..944.1606.1013..653..676

%F ..821..574..652..926..557..460..574..778..588..678.1013..656..536..660

%F ..768..610..653..746..592..495..601..791..594..575..653..536..478..584

%F ..666..652..599..628..598..560..726..896..990..726..676..660..584..652

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Aug 24 2015

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)