The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A259742

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

#6 by R. H. Hardin at Sat Jul 04 09:03:09 EDT 2015

STATUS

editing

approved

#5 by R. H. Hardin at Sat Jul 04 09:03:05 EDT 2015

LINKS

R. H. Hardin, <a href="/A259742/b259742.txt">Table of n, a(n) for n = 1..1042</a>

#4 by R. H. Hardin at Sat Jul 04 09:02:41 EDT 2015

LINKS

R. H. Hardin, <a href="/A259742/a259742.txt">TITLE FOR LINK</a>

#3 by R. H. Hardin at Sat Jul 04 09:02:19 EDT 2015

LINKS

R. H. Hardin, <a href="/A259742/a259742.txt">TITLE FOR LINK</a>

#2 by R. H. Hardin at Sat Jul 04 09:02:03 EDT 2015

NAME

allocated for R. H. Hardin

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

DATA

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

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

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin, Jul 04 2015

STATUS

approved

editing

#1 by R. H. Hardin at Sat Jul 04 08:54:26 EDT 2015

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved