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A229402 T(n,k)=Number of nXk 0..2 arrays with top left element 0, horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and antidiagonal differences never 0 7
1, 2, 2, 4, 5, 4, 8, 13, 13, 8, 16, 34, 44, 34, 16, 32, 89, 153, 153, 89, 32, 64, 233, 536, 711, 536, 233, 64, 128, 610, 1881, 3357, 3357, 1881, 610, 128, 256, 1597, 6604, 15952, 21464, 15952, 6604, 1597, 256, 512, 4181, 23189, 75965, 138645, 138645, 75965 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2.....4......8......16.......32.........64.........128..........256

...2....5....13.....34......89......233........610........1597.........4181

...4...13....44....153.....536.....1881.......6604.......23189........81428

...8...34...153....711....3357....15952......75965......362012......1725628

..16...89...536...3357...21464...138645.....899860.....5852687.....38099072

..32..233..1881..15952..138645..1220881...10826489....96353860....859094433

..64..610..6604..75965..899860.10826489..131393852..1602580515..19601243880

.128.1597.23189.362012.5852687.96353860.1602580515.26816872052.450388122809

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..684

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: a(n) = 5*a(n-1) -6*a(n-2) +3*a(n-3) -a(n-4)

k=4: [order 8]

k=5: [order 16]

k=6: [order 32]

k=7: [order 64]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1)

Column 2 is A001519(n+1)

Sequence in context: A115216 A208637 A252938 * A266249 A276299 A231302

Adjacent sequences:  A229399 A229400 A229401 * A229403 A229404 A229405

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Sep 22 2013

STATUS

approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)