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A171847 Total area under all peakless Motzkin paths of length n (n>=0). 1
0, 0, 0, 2, 7, 22, 68, 198, 563, 1578, 4367, 11980, 32648, 88500, 238886, 642598, 1723629, 4612170, 12316357, 32832302, 87390763, 232305470, 616812557, 1636084020, 4335770052, 11480937084, 30379110906, 80332372838, 212300488377 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n) = Sum_{k>=0} k*A171846(n,k).

G.f.: z^2*(g^2 -1)/((1+z+z^2)(1-3z+z^2)), where g=g(z) satisfies g = 1 + zg + z^2*g(g - 1).

EXAMPLE

a(4)=7 because the areas under the paths HHHH, HUHD, UHHD and UHDH are 0, 2, 3 and 2, respectively.

MAPLE

g := ((1-z+z^2-sqrt(1-2*z-z^2-2*z^3+z^4))*1/2)/z^2: G := z^2*(g^2-1)/((1+z+z^2)*(1-3*z+z^2)): Gser := series(G, z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 30);

CROSSREFS

Cf. A004148, A171846.

Sequence in context: A071684 A290917 A060816 * A037552 A308113 A291012

Adjacent sequences:  A171844 A171845 A171846 * A171848 A171849 A171850

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 08 2010

STATUS

approved

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Last modified September 15 18:47 EDT 2019. Contains 327083 sequences. (Running on oeis4.)