A255622 T(n,k)=Number of length n+k 0..2 arrays with at most two downsteps in every k consecutive neighbor pairs

9, 27, 27, 81, 81, 81, 237, 243, 243, 243, 651, 694, 729, 729, 729, 1647, 1803, 2040, 2187, 2187, 2187, 3834, 4248, 5088, 5997, 6561, 6561, 6561, 8272, 9186, 11386, 14381, 17622, 19683, 19683, 19683, 16698, 18483, 23298, 30816, 40659, 51768, 59049, 59049

Offset

1,1

Comments

Table starts

......9.....27......81.....237.....651.....1647.....3834.....8272....16698

.....27.....81.....243.....694....1803.....4248.....9186....18483....35016

.....81....243.....729....2040....5088....11386....23298....44361....79692

....243....729....2187....5997...14381....30816....60390...110270...190269

....729...2187....6561...17622...40659....83325...156563...275166...458604

...2187...6561...19683...51768..114546...225253...405687...685713..1103630

...6561..19683...59049..152106..322078...602886..1047141..1706242..2653107

..19683..59049..177147..446932..907110..1605726..2656032..4203558..6343974

..59049.177147..531441.1313199.2556858..4293918..6682971.10111362.14922893

.177147.531441.1594323.3858468.7205734.11529741.16925280.24065191.34121019

Links

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

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 3*a(n-1) -a(n-3) +3*a(n-4) -3*a(n-5) -8*a(n-6) +9*a(n-7) -3*a(n-8) +a(n-9)

k=5: [order 14]

k=6: [order 20]

k=7: [order 30]

Empirical for row n:

n=1: [polynomial of degree 8]

n=2: [polynomial of degree 8]

n=3: [polynomial of degree 8]

n=4: [polynomial of degree 8] for n>2

n=5: [polynomial of degree 8] for n>3

n=6: [polynomial of degree 8] for n>4

n=7: [polynomial of degree 8] for n>5

Example

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

Crossrefs

Column 1 is A000244(n+1)

Column 2 is A000244(n+2)

Column 3 is A000244(n+3)

Sequence in context: A010817 A205973 A122985 * A209511 A370872 A115148

Adjacent sequences: A255619 A255620 A255621 * A255623 A255624 A255625

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 28 2015

Status

approved