A259742 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00010101 or 01010101

20, 22, 22, 42, 36, 42, 62, 74, 74, 62, 101, 136, 190, 136, 101, 152, 230, 374, 374, 230, 152, 265, 414, 792, 868, 792, 414, 265, 382, 760, 1514, 1882, 1882, 1514, 760, 382, 652, 1356, 3480, 4456, 4904, 4456, 3480, 1356, 652, 962, 2414, 6542, 10570, 12086, 12086

Offset

1,1

Comments

Table starts

..20...22....42.....62....101.....152......265......382.......652........962

..22...36....74....136....230.....414......760.....1356......2414.......4348

..42...74...190....374....792....1514.....3480.....6542.....14580......27866

..62..136...374....868...1882....4456....10570....24150.....55686.....130032

.101..230...792...1882...4904...12086....35036....82492....230779.....558772

.152..414..1514...4456..12086...36522...110886...321402....940024....2797222

.265..760..3480..10570..35036..110886...416107..1244504...4489732...13887332

.382.1356..6542..24150..82492..321402..1244504..4569918..17054488...64800792

.652.2414.14580..55686.230779..940024..4489732.17054488..77901650..308237826

.962.4348.27866.130032.558772.2797222.13887332.64800792.308237826.1497446190

Links

R. H. Hardin, Table of n, a(n) for n = 1..1042

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-3) +a(n-4)

k=3: a(n) = 2*a(n-2) +9*a(n-4) +4*a(n-6) -6*a(n-8) +4*a(n-10) for n>11

k=4: [order 10] for n>11

k=5: [order 18] for n>19

k=6: [order 20] for n>22

k=7: [order 34] for n>37

Example

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

Crossrefs

Sequence in context: A041838 A128356 A109212 * A050653 A267510 A095453

Adjacent sequences: A259739 A259740 A259741 * A259743 A259744 A259745

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 04 2015

Status

approved