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A191393 Number of dispersed Dyck paths of length n (i.e., of Motzkin paths of length n with no (1,0)-steps at positive heights) having no base pyramids. A base pyramid is a factor of the form U^j D^j (j>0), starting at the horizontal axis. Here U=(1,1) and D=(1,-1). 3
1, 1, 1, 1, 1, 1, 2, 3, 8, 13, 31, 49, 109, 170, 371, 581, 1270, 2010, 4417, 7063, 15581, 25123, 55554, 90179, 199752, 326089, 723351, 1186670, 2635764, 4342829, 9657336, 15973459, 35558165, 59017088, 131500422, 218932442, 488234057, 815127111, 1819186163 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n) = A191392(n,0).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (2*(1-z^2))/(1-2*z+z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2)).

a(n) ~ 9 * 2^(n-11/2) * (16+(-1)^n) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 20 2014

EXAMPLE

a(7)=3 because we have HHHHHHH, HUUDUDD, and UUDUDDH, where U=(1,1), D=(1,-1), and H=(1,0).

MAPLE

g := (2*(1-z^2))/(1-2*z+z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2)): gser := series(g, z = 0, 42): seq(coeff(gser, z, n), n = 0 .. 38);

MATHEMATICA

CoefficientList[Series[(2*(1-x^2))/(1-2*x+x^2+2*x^3+(1-x^2)*Sqrt[1-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 20 2014 *)

PROG

(MAGMA) m:=40; R<x>:=LaurentSeriesRing(RationalField(), m); Coefficients(R! (2*(1-x^2))/(1-2*x+x^2+2*x^3+(1-x^2)*Sqrt(1-4*x^2))); // Vincenzo Librandi, Mar 21 2014

CROSSREFS

Cf. A191392.

Sequence in context: A045692 A103196 A113954 * A025082 A317911 A151889

Adjacent sequences:  A191390 A191391 A191392 * A191394 A191395 A191396

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 04 2011

STATUS

approved

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Last modified January 29 01:49 EST 2020. Contains 331328 sequences. (Running on oeis4.)