A255660 T(n,k)=Number of length n+k 0..3 arrays with at most two downsteps in every k consecutive neighbor pairs

16, 64, 64, 255, 256, 256, 968, 1016, 1024, 1024, 3340, 3692, 4048, 4096, 4096, 10320, 11752, 14192, 16128, 16384, 16384, 28722, 33042, 42653, 54560, 64257, 65536, 65536, 72920, 83752, 112196, 155144, 209412, 256012, 262144, 262144, 171106, 195020

Offset

1,1

Comments

Table starts

......16.......64......255.......968......3340.....10320.....28722......72920

......64......256.....1016......3692.....11752.....33042.....83752.....195020

.....256.....1024.....4048.....14192.....42653....112196....265430.....577464

....1024.....4096....16128.....54560....155144....385738....864924....1788660

....4096....16384....64257....209412....564600...1324872...2816673....5555336

...16384....65536...256012....803246...2036844...4542671...9169016...17232696

...65536...262144..1020000...3083292...7323894..15269184..29577432...53275408

..262144..1048576..4063872..11835664..26452984..50963540..92530816..161617336

.1048576..4194304.16191231..45429680..95690028.171784096.286454024..471810032

.4194304.16777216.64508912.174365744.345980784.583245999.900260308.1359483102

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 4*a(n-1)

k=3: a(n) = 4*a(n-1) -a(n-4)

k=4: [order 12]

k=5: [order 24]

k=6: [order 35]

k=7: [order 48]

Empirical for row n:

n=1: [polynomial of degree 11]

n=2: [polynomial of degree 11]

n=3: [polynomial of degree 11] for n>1

n=4: [polynomial of degree 11] for n>2

n=5: [polynomial of degree 11] for n>3

n=6: [polynomial of degree 11] for n>4

n=7: [polynomial of degree 11] for n>5

Example

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

Crossrefs

Column 1 is A000302(n+1)

Column 2 is A000302(n+2)

Column 3 is A206450(n+3)

Sequence in context: A250102 A322032 A090567 * A303797 A118902 A092210

Adjacent sequences: A255657 A255658 A255659 * A255661 A255662 A255663

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2015

Status

approved