|
| |
|
|
A200869
|
|
Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
|
|
1
|
|
|
|
161, 595, 2163, 7973, 29325, 107777, 395929, 1454643, 5344795, 19638715, 72159035, 265134245, 974183489, 3579448271, 13151993143, 48324463973, 177558916493, 652405957937, 2397139747601, 8807827288183, 32362661242755, 118910351874471
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical: a(n) = 4*a(n-1) -3*a(n-2) +4*a(n-3) +9*a(n-4) +7*a(n-6) +6*a(n-7) +a(n-8) +2*a(n-9) +a(n-10).
Empirical g.f.: x*(161 - 49*x + 266*x^2 + 462*x^3 + 93*x^4 + 389*x^5 + 310*x^6 + 70*x^7 + 105*x^8 + 49*x^9) / (1 - 4*x + 3*x^2 - 4*x^3 - 9*x^4 - 7*x^6 - 6*x^7 - x^8 - 2*x^9 - x^10). - Colin Barker, Oct 16 2017
|
|
|
EXAMPLE
|
Some solutions for n=3
..6....3....0....5....3....0....6....6....2....5....5....2....6....0....5....5
..6....2....4....1....3....0....6....2....3....2....3....0....4....1....0....2
..5....2....4....0....2....6....6....2....5....2....1....0....0....1....0....2
..3....3....4....0....2....6....1....3....5....1....1....3....0....2....2....6
..2....4....4....5....5....3....0....6....4....0....3....3....0....5....3....6
|
|
|
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, 7}]; a[n_] := Sum[a[n, x, y], {x, 7}, {y, 7}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
