A259770 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 or 00000101

32, 49, 49, 104, 87, 104, 201, 167, 167, 201, 376, 299, 256, 299, 376, 745, 564, 385, 385, 564, 745, 1494, 1086, 612, 451, 612, 1086, 1494, 2897, 2045, 1108, 474, 474, 1108, 2045, 2897, 5610, 3870, 1708, 835, 400, 835, 1708, 3870, 5610, 11065, 7371, 2700, 872

Offset

1,1

Comments

Table starts

....32....49..104..201.376..745.1494.2897.5610.11065.21780.42461.82984.162977

....49....87..167..299.564.1086.2045.3870.7371.14001.26647.50766.96574.183815

...104...167..256..385.612.1108.1708.2700.4660..7378.11350.19232.31280..48032

...201...299..385..451.474..835..872..968.1532..1794..2116..2746..4218...4546

...376...564..612..474.400..798..524..450..588...644...540...568..1060....716

...745..1086.1108..835.798.1805..654..436..544...634...528...688..1512....478

..1494..2045.1708..872.524..654..480..392..492...536...424...420...532....402

..2897..3870.2700..968.450..436..392..336..368...428...404...410...430....416

..5610..7371.4660.1532.588..544..492..368..384...362...456...404...404....424

.11065.14001.7378.1794.644..634..536..428..362...368...438...398...404....366

Links

R. H. Hardin, Table of n, a(n) for n = 1..1248

Formula

Empirical for column k:

k=1: a(n) = a(n-2) +2*a(n-3) +6*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8) for n>9

k=2: [order 11] for n>12

k=3: [order 14] for n>17

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>24

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-1) -a(n-2) +a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11) -a(n-12) +a(n-13) for n>20

Empirical periodic continuations for column k:

k=6: period of length 14 starting at n=8: 436 544 634 528 688 1512 478 442 570 726 674 764 1724 590

k=7: period of length 14 starting at n=8: 392 492 536 424 420 532 402 344 420 500 416 412 566 448

Example

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

Crossrefs

Sequence in context: A236330 A045023 A222300 * A066472 A140172 A259765

Adjacent sequences: A259767 A259768 A259769 * A259771 A259772 A259773

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 04 2015

Status

approved