|
| |
|
|
A057585
|
|
Area under Motzkin excursions.
|
|
2
| |
|
|
0, 1, 4, 16, 56, 190, 624, 2014, 6412, 20219, 63284, 196938, 610052, 1882717, 5792528, 17776102, 54433100, 166374109, 507710420, 1547195902, 4709218604, 14318240578, 43493134160, 132003957436, 400337992056, 1213314272395
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| a(n) is the sum of areas under all Motzkin excursions of length n. (nonnegative walks beginning and ending in 0, with jumps -1,0,+1)
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..400
C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.
|
|
|
FORMULA
| G.f.=(x^2+2*x-1+(-x+1)*sqrt((x+1)*(1-3*x)))/(2*(3*x-1)*(x+1)*x^2)
|
|
|
MAPLE
| G:= (x^2+2*x-1+(-x+1)*sqrt((x+1)*(1-3*x)))/(2*(3*x-1)*(x+1)*x^2): Gser:=series(G, x=0, 30): seq(coeff(Gser, x, n), n=1..26); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 08 2007
|
|
|
MATHEMATICA
| f[x_] := (x^2+2*x-1+(-x+1)*Sqrt[(x+1)*(1-3*x)]) / (2*(3*x-1)*(x+1)*x^2); Drop[ CoefficientList[ Series[ f[x], {x, 0, 26}], x], 1] (* From Jean-François Alcover, Dec 21 2011, from g.f. *)
|
|
|
CROSSREFS
| Sequence in context: A026126 A026155 A025182 * A097128 A006079 A201619
Adjacent sequences: A057582 A057583 A057584 * A057586 A057587 A057588
|
|
|
KEYWORD
| easy,nonn,nice
|
|
|
AUTHOR
| Cyril Banderier (Cyril.Banderier(AT)inria.fr), Oct 04 2000
|
| |
|
|
