A258730 T(n,k)=Number of length n+k 0..3 arrays with at most one downstep in every k consecutive neighbor pairs

16, 60, 64, 190, 225, 256, 512, 608, 840, 1024, 1212, 1408, 2028, 3136, 4096, 2592, 2936, 4184, 6552, 11704, 16384, 5115, 5664, 7834, 12549, 20955, 43681, 65536, 9460, 10280, 13720, 21860, 35540, 68120, 163020, 262144, 16588, 17754, 22866, 35704

Offset

1,1

Comments

Table starts

......16......60.....190.....512....1212....2592....5115....9460....16588

......64.....225.....608....1408....2936....5664...10280...17754....29416

.....256.....840....2028....4184....7834...13720...22866...36656....56925

....1024....3136....6552...12549...21860...35704...55660...83758...122584

....4096...11704...20955...35540...59188...92548..138196..199264...279560

...16384...43681...68120...98676..149960..228081..331584..465580...635992

...65536..163020..220854..281136..370510..526672..752180.1038256..1394568

..262144..608400..711432..819453..941024.1183616.1607656.2192682..2911776

.1048576.2270580.2300008.2358888.2487276.2727288.3343894.4392072..5783522

.4194304.8473921.7446144.6678576.6650600.6597449.7100132.8569478.10965340

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) -4*a(n-3) +a(n-4)

k=3: [order 8]

k=4: [order 12]

k=5: [order 16]

k=6: [order 19]

k=7: [order 22]

Empirical for row n:

n=1: [polynomial of degree 7]

n=2: [polynomial of degree 7]

n=3: [polynomial of degree 7] for n>1

n=4: [polynomial of degree 7] for n>2

n=5: [polynomial of degree 7] for n>3

n=6: [polynomial of degree 7] for n>4

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

Example

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

Crossrefs

Column 1 is A000302(n+1)

Column 2 is A072335(n+2)

Sequence in context: A063521 A027117 A292537 * A187173 A296958 A258731

Adjacent sequences: A258727 A258728 A258729 * A258731 A258732 A258733

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 08 2015

Status

approved