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A307577 Number of Motzkin meanders of length n with an odd number of peaks. 2
0, 0, 1, 4, 13, 40, 119, 348, 1011, 2928, 8471, 24516, 71023, 206024, 598513, 1741332, 5073733, 14804160, 43252855, 126526756, 370551287, 1086365336, 3188090101, 9364411252, 27529374201, 80993754352, 238463467529, 702563144252, 2071200546129, 6109619428824 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A Motzkin meander is a lattice path with steps from the set {D=-1, H=0, U=1} that starts at (0,0), and never goes below the x-axis.
A peak is an occurrence of the pattern UD.
LINKS
FORMULA
G.f.: (sqrt((1+t)*(1-3*t))/(1-3*t) - sqrt((1-t)*(1-2*t)*(1+t+2*t^2))/((1-t)*(1-2*t))) / (4*t).
EXAMPLE
For n = 3 the a(3) = 4 paths are UDH, HUD, UDU, UUD.
MAPLE
b:= proc(x, y, t, c) option remember; `if`(y<0, 0, `if`(x=0, c,
b(x-1, y-1, 0, irem(c+t, 2))+b(x-1, y, 0, c)+b(x-1, y+1, 1, c)))
end:
a:= n-> b(n, 0$3):
seq(a(n), n=0..35); # Alois P. Heinz, Apr 16 2019
MATHEMATICA
b[x_, y_, t_, c_] := b[x, y, t, c] = If[y<0, 0, If[x==0, c, b[x-1, y-1, 0, Mod[c+t, 2]] + b[x-1, y, 0, c] + b[x-1, y+1, 1, c]]];
a[n_] := b[n, 0, 0, 0];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 29 2019, after Alois P. Heinz *)
CROSSREFS
Cf. A001006.
Sequence in context: A191132 A360606 A119915 * A137744 A027130 A027121
KEYWORD
nonn
AUTHOR
Andrei Asinowski, Apr 15 2019
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)