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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.

%I A258730 #6 Jul 23 2025 15:31:33
%S A258730 16,60,64,190,225,256,512,608,840,1024,1212,1408,2028,3136,4096,2592,
%T A258730 2936,4184,6552,11704,16384,5115,5664,7834,12549,20955,43681,65536,
%U A258730 9460,10280,13720,21860,35540,68120,163020,262144,16588,17754,22866,35704
%N A258730 T(n,k)=Number of length n+k 0..3 arrays with at most one downstep in every k consecutive neighbor pairs.
%C A258730 Table starts
%C A258730 ......16......60.....190.....512....1212....2592....5115....9460....16588
%C A258730 ......64.....225.....608....1408....2936....5664...10280...17754....29416
%C A258730 .....256.....840....2028....4184....7834...13720...22866...36656....56925
%C A258730 ....1024....3136....6552...12549...21860...35704...55660...83758...122584
%C A258730 ....4096...11704...20955...35540...59188...92548..138196..199264...279560
%C A258730 ...16384...43681...68120...98676..149960..228081..331584..465580...635992
%C A258730 ...65536..163020..220854..281136..370510..526672..752180.1038256..1394568
%C A258730 ..262144..608400..711432..819453..941024.1183616.1607656.2192682..2911776
%C A258730 .1048576.2270580.2300008.2358888.2487276.2727288.3343894.4392072..5783522
%C A258730 .4194304.8473921.7446144.6678576.6650600.6597449.7100132.8569478.10965340
%H A258730 R. H. Hardin, <a href="/A258730/b258730.txt">Table of n, a(n) for n = 1..9999</a>
%F A258730 Empirical for column k:
%F A258730 k=1: a(n) = 4*a(n-1)
%F A258730 k=2: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4)
%F A258730 k=3: [order 8]
%F A258730 k=4: [order 12]
%F A258730 k=5: [order 16]
%F A258730 k=6: [order 19]
%F A258730 k=7: [order 22]
%F A258730 Empirical for row n:
%F A258730 n=1: [polynomial of degree 7]
%F A258730 n=2: [polynomial of degree 7]
%F A258730 n=3: [polynomial of degree 7] for n>1
%F A258730 n=4: [polynomial of degree 7] for n>2
%F A258730 n=5: [polynomial of degree 7] for n>3
%F A258730 n=6: [polynomial of degree 7] for n>4
%F A258730 n=7: [polynomial of degree 7] for n>5
%e A258730 Some solutions for n=4 k=4
%e A258730 ..1....1....0....0....3....0....1....3....2....0....2....3....0....3....2....0
%e A258730 ..0....2....3....3....1....1....2....3....2....1....2....2....3....3....0....2
%e A258730 ..2....0....3....1....1....1....3....3....0....1....3....3....0....0....2....2
%e A258730 ..3....2....3....1....2....1....1....0....0....1....0....3....1....2....3....3
%e A258730 ..3....3....3....1....2....1....1....0....1....1....0....3....3....3....3....0
%e A258730 ..0....3....3....2....3....3....1....1....1....0....3....0....3....3....2....0
%e A258730 ..0....3....1....3....0....0....2....3....2....0....3....2....1....0....2....2
%e A258730 ..3....2....2....1....2....1....0....1....0....0....2....2....1....0....2....2
%Y A258730 Column 1 is A000302(n+1)
%Y A258730 Column 2 is A072335(n+2)
%K A258730 nonn,tabl
%O A258730 1,1
%A A258730 _R. H. Hardin_, Jun 08 2015