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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
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: A208637 A341867 A252938 * A266249 A276299 A231302
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Sep 22 2013
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)