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A258730 T(n,k)=Number of length n+k 0..3 arrays with at most one downstep in every k consecutive neighbor pairs 13
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 08 2015
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)