|
|
A200868
|
|
Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
|
|
1
|
|
|
106, 356, 1168, 3886, 12890, 42744, 141688, 469726, 1557320, 5163158, 17117854, 56752072, 188154290, 623802050, 2068138180, 6856654898, 22732385492, 75366392740, 249867889178, 828405870894, 2746476505360, 9105600837300
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 3*a(n-1) + a(n-3) + 7*a(n-4) + 3*a(n-5) + 2*a(n-6) + 3*a(n-7) + a(n-8).
Empirical g.f.: 2*x*(53 + 19*x + 50*x^2 + 138*x^3 + 67*x^4 + 48*x^5 + 57*x^6 + 18*x^7) / (1 - 3*x - x^3 - 7*x^4 - 3*x^5 - 2*x^6 - 3*x^7 - x^8). - Colin Barker, Oct 16 2017
|
|
EXAMPLE
|
Some solutions for n=3
..0....3....5....1....1....4....0....5....1....3....5....3....5....2....0....3
..1....0....5....1....0....0....2....3....1....5....0....0....2....0....0....5
..4....0....5....1....0....0....5....2....3....5....0....0....1....0....2....5
..4....1....5....0....0....2....5....2....3....2....3....2....1....5....3....4
..4....1....4....0....2....5....5....5....4....2....4....5....3....5....4....0
|
|
MATHEMATICA
|
a[0, x_, y_] := 1; a[n_, x_, y_] := a[n, x, y] = Sum[If[z <= x <= y || y <= x <= z, a[n - 1, z, x], 0], {z, 6}]; a[n_] := Sum[a[n, x, y], {x, 6}, {y, 6}]; Array[a, 25] (* Giovanni Resta, Mar 06 2014 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|