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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

%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

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Last modified May 29 01:39 EDT 2022. Contains 354122 sequences. (Running on oeis4.)