A206094 T(n,k) = number of (n+1) X (k+1) 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly two counterclockwise and two clockwise edge increases.

81, 270, 270, 972, 780, 972, 3564, 2016, 2016, 3564, 13608, 5952, 4560, 5952, 13608, 52812, 17976, 13344, 13344, 17976, 52812, 205416, 54432, 33792, 48816, 33792, 54432, 205416, 803844, 165936, 86496, 131904, 131904, 86496, 165936, 803844

Offset

1,1

Comments

Table starts

.....81....270....972....3564....13608.....52812.....205416......803844

....270....780...2016....5952....17976.....54432.....165936......504912

....972...2016...4560...13344....33792.....86496.....240192......608256

...3564...5952..13344...48816...131904....444480....1645920.....4484736

..13608..17976..33792..131904...516912...2156544....8613504....34039392

..52812..54432..86496..444480..2156544..10584000...56633472...279244800

.205416.165936.240192.1645920..8613504..56633472..408445632..2199502080

.803844.504912.608256.4484736.34039392.279244800.2199502080.17222950080

Links

R. H. Hardin, Table of n, a(n) for n = 1..839

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -a(n-2) +12*a(n-3) -36*a(n-4)

k=2: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -10*a(n-4) for n>6

k=3: a(n) = 18*a(n-3) for n>6

k=4: a(n) = 34*a(n-3) for n>7

k=5: a(n) = 66*a(n-3) for n>8

k=6: a(n) = 130*a(n-3) for n>9

k=7: a(n) = 258*a(n-3) for n>10

apparently a(n) = (2+2^(k+1))*a(n-3) for k>2 and n>k+3

Example

Some solutions for n=4, k=3:
..2..0..0..2....0..2..0..2....2..1..0..2....2..2..0..2....0..0..1..2
..1..2..0..0....1..0..0..2....1..0..0..2....0..2..2..0....1..0..0..1
..1..1..2..0....0..0..1..0....0..0..1..0....1..0..2..2....0..1..0..0
..2..1..1..2....0..2..0..0....0..2..0..0....1..1..0..2....0..0..2..2
..0..2..1..1....1..0..0..1....2..0..0..1....2..1..1..0....1..0..2..1

Crossrefs

Sequence in context: A236739 A237234 A237227 * A202333 A207042 A206087

Adjacent sequences: A206091 A206092 A206093 * A206095 A206096 A206097

Keyword

nonn,tabl

Author

R. H. Hardin Feb 03 2012

Status

approved