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

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

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