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

Author

R. H. Hardin, Mar 01 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302(n+1)

Column 2 is A000302(n+2)

Column 3 is A206450(n+3)

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