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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 08:31 EST 2021. Contains 349594 sequences. (Running on oeis4.)