This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A258730 T(n,k)=Number of length n+k 0..3 arrays with at most one downstep in every k consecutive neighbor pairs 13

%I

%S 16,60,64,190,225,256,512,608,840,1024,1212,1408,2028,3136,4096,2592,

%T 2936,4184,6552,11704,16384,5115,5664,7834,12549,20955,43681,65536,

%U 9460,10280,13720,21860,35540,68120,163020,262144,16588,17754,22866,35704

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

%C Table starts

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

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

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

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

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

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

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

%C ..262144..608400..711432..819453..941024.1183616.1607656.2192682..2911776

%C .1048576.2270580.2300008.2358888.2487276.2727288.3343894.4392072..5783522

%C .4194304.8473921.7446144.6678576.6650600.6597449.7100132.8569478.10965340

%H R. H. Hardin, <a href="/A258730/b258730.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4)

%F k=3: [order 8]

%F k=4: [order 12]

%F k=5: [order 16]

%F k=6: [order 19]

%F k=7: [order 22]

%F Empirical for row n:

%F n=1: [polynomial of degree 7]

%F n=2: [polynomial of degree 7]

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

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

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

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

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

%e Some solutions for n=4 k=4

%e ..1....1....0....0....3....0....1....3....2....0....2....3....0....3....2....0

%e ..0....2....3....3....1....1....2....3....2....1....2....2....3....3....0....2

%e ..2....0....3....1....1....1....3....3....0....1....3....3....0....0....2....2

%e ..3....2....3....1....2....1....1....0....0....1....0....3....1....2....3....3

%e ..3....3....3....1....2....1....1....0....1....1....0....3....3....3....3....0

%e ..0....3....3....2....3....3....1....1....1....0....3....0....3....3....2....0

%e ..0....3....1....3....0....0....2....3....2....0....3....2....1....0....2....2

%e ..3....2....2....1....2....1....0....1....0....0....2....2....1....0....2....2

%Y Column 1 is A000302(n+1)

%Y Column 2 is A072335(n+2)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jun 08 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)