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A209534 T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences 6
5, 9, 9, 17, 25, 17, 33, 65, 65, 33, 65, 193, 257, 193, 65, 129, 513, 1025, 1025, 513, 129, 257, 1537, 4097, 6145, 4097, 1537, 257, 513, 4097, 16385, 32769, 32769, 16385, 4097, 513, 1025, 12289, 65537, 196609, 262145, 196609, 65537, 12289, 1025, 2049, 32769 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...5.....9.....17......33........65........129.........257...........513

...9....25.....65.....193.......513.......1537........4097.........12289

..17....65....257....1025......4097......16385.......65537........262145

..33...193...1025....6145.....32769.....196609.....1048577.......6291457

..65...513...4097...32769....262145....2097153....16777217.....134217729

.129..1537..16385..196609...2097153...25165825...268435457....3221225473

.257..4097..65537.1048577..16777217..268435457..4294967297...68719476737

.513.12289.262145.6291457.134217729.3221225473.68719476737.1649267441665

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..7808

FORMULA

Empirical: for odd columns k T(n,k) = 2^((n+1)*(k+1)/2)+1

Empirical for even columns k:

k=2: a(n) = a(n-1) +8*a(n-2) -8*a(n-3)

k=4: a(n) = a(n-1) +32*a(n-2) -32*a(n-3)

k=6: a(n) = a(n-1) +128*a(n-2) -128*a(n-3)

Apparently for even k a(n) = a(n-1) +2^(k+1)*a(n-2) -2^(k+1)*a(n-3)

EXAMPLE

Some solutions for n=4 k=3

..1..2..1..2....0..1..2..1....2..0..2..0....1..2..1..2....0..1..0..1

..2..1..0..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2

..1..2..1..0....2..1..0..1....2..0..2..0....1..2..1..2....2..1..0..1

..2..1..2..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2

..1..2..1..2....2..1..0..1....2..0..2..0....1..2..1..0....2..1..0..1

CROSSREFS

Column 1 is A000051(n+1)

Column 3 is A052539(n+1)

Column 5 is A062395(n+1)

Sequence in context: A057655 A175374 A141124 * A046255 A068388 A314582

Adjacent sequences:  A209531 A209532 A209533 * A209535 A209536 A209537

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 10 2012

STATUS

approved

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Last modified August 11 03:22 EDT 2020. Contains 336421 sequences. (Running on oeis4.)