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.

48, 80, 80, 170, 132, 170, 336, 269, 269, 336, 652, 484, 516, 484, 652, 1293, 871, 754, 754, 871, 1293, 2588, 1702, 1210, 769, 1210, 1702, 2588, 5100, 3230, 2187, 816, 816, 2187, 3230, 5100, 9996, 6084, 3436, 1286, 656, 1286, 3436, 6084, 9996, 19788, 11656

Offset

1,1

Comments

Table starts

....48....80...170..336..652.1293.2588.5100..9996.19788.39102.76977.151492

....80...132...269..484..871.1702.3230.6084.11656.22140.41998.80163.152575

...170...269...516..754.1210.2187.3436.5368..9414.14902.22538.38820..62948

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

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

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

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

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

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

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..3609

Formula

Empirical for column k:

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

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

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

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

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

k=6: a(n) = a(n-14) for n>23

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

Empirical apparent periods for column k:

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

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

Empirical apparent period for diagonal:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Example

Some solutions for n=4 k=4
..0..1..0..1..0..0....1..0..0..0..0..1....0..0..1..0..0..0....0..0..1..0..1..0
..0..0..1..0..0..0....0..1..0..0..1..0....0..0..0..0..0..1....0..1..0..0..1..0
..0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..0..0..0..0..0..1....0..0..0..0..0..0....0..0..1..0..0..1....0..0..0..0..0..0
..0..0..1..0..0..0....0..0..0..1..0..0....0..1..0..0..0..0....0..0..1..0..0..1
..0..1..0..0..0..0....0..0..1..0..0..0....0..0..0..0..0..1....0..1..0..0..0..0

Crossrefs

Sequence in context: A261704 A260370 A260363 * A335281 A335196 A348527

Adjacent sequences: A261550 A261551 A261552 * A261554 A261555 A261556

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 24 2015

Status

approved