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A200865
Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
1
17, 37, 77, 163, 343, 723, 1523, 3209, 6761, 14245, 30013, 63235, 133231, 280707, 591427, 1246089, 2625409, 5531525, 11654477, 24555043, 51735495, 109002515, 229659507, 483874057, 1019483609, 2147969733, 4525598973, 9535072003
OFFSET
1,1
COMMENTS
Column 2 of A200871.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) +a(n-4).
Empirical g.f.: x*(17 + 3*x + 3*x^2 + 9*x^3) / (1 - 2*x - x^4). - Colin Barker, Oct 15 2017
EXAMPLE
Some solutions for n=3
..0....2....0....2....2....0....0....0....0....1....2....2....0....0....0....2
..0....2....0....2....1....1....0....1....1....0....2....0....2....0....2....1
..1....2....2....1....0....2....0....1....1....0....1....0....2....0....2....1
..2....2....2....1....0....2....0....2....0....1....1....1....2....1....2....1
..2....2....0....2....0....2....2....2....0....1....1....2....2....2....0....1
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, 3}]; a[n_] := Sum[a[n, x, y], {x, 3}, {y, 3}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)
CROSSREFS
Sequence in context: A050952 A256517 A323603 * A319245 A093930 A048880
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 23 2011
STATUS
approved