A261709 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.

48, 76, 76, 172, 134, 172, 338, 270, 270, 338, 628, 462, 468, 462, 628, 1298, 892, 662, 662, 892, 1298, 2752, 1751, 1168, 675, 1168, 1751, 2752, 5526, 3299, 2372, 734, 734, 2372, 3299, 5526, 10972, 6324, 3700, 1443, 676, 1443, 3700, 6324, 10972, 22462

Offset

1,1

Comments

Table starts

....48....76...172..338..628.1298.2752.5526.10972.22462.46160.93354.188556

....76...134...270..462..892.1751.3299.6324.12389.23874.46352.90232.175147

...172...270...468..662.1168.2372.3700.6158.11812.19350.31112.58428..98160

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

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

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

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

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

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

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..3274

Formula

Empirical for column k:

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

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

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

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

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>21

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

Empirical periodic continuations for column k:

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

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

Empirical periodic continuations for diagonal:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Example

Some solutions for n=7 k=4
..0..0..0..0..0..1....1..0..1..0..1..0....1..0..0..1..0..0....1..0..0..0..0..0
..1..0..0..0..1..0....0..1..0..0..0..0....0..0..0..0..0..0....0..1..0..0..0..1
..0..1..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..0..0..0..1..0....0..0..1..0..0..1....0..0..0..0..0..0
..0..0..0..0..1..0....1..0..0..1..0..0....0..1..0..0..0..0....0..1..0..0..0..0
..1..0..0..1..0..0....0..0..0..0..0..0....0..0..0..0..0..1....0..0..1..0..0..1
..0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..0..0
..0..0..0..0..0..0....0..0..0..1..0..0....0..1..0..0..0..0....0..0..0..0..0..1
..0..0..1..0..0..1....1..0..0..0..1..0....1..0..0..0..0..0....0..1..0..0..1..1

Crossrefs

Sequence in context: A005276 A328370 A143722 * A261704 A260370 A260363

Adjacent sequences: A261706 A261707 A261708 * A261710 A261711 A261712

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 28 2015

Status

approved