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A187260 Number of uh^jd's for some j>0, starting at level 0, where u=(1,1), h=(1,0), and d=(1,-1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology). 1
0, 0, 0, 1, 3, 6, 12, 25, 53, 115, 255, 575, 1315, 3043, 7111, 16756, 39766, 94961, 228003, 550081, 1332839, 3241930, 7913028, 19375635, 47579847, 117149125, 289142441, 715253644, 1773011502, 4403539181, 10956537307, 27307002454, 68164324150, 170404155586, 426584025250, 1069289177950 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)=Sum(k*A098071(n,k), k>=0).

The terms a(n), starting from n=3, are the partial sums of the sequence A089735.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

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

EXAMPLE

a(4)=3 because the 4 (=A004148(4)) peakless Motzkin paths of length 4, namely hhhh, h(uhd), (uhd)h, and (uhhd) contain 0+1+1+1 subwords of type uh^ju for some j>0, starting at level 0 (shown between parentheses.

MAPLE

eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): F := z^3*g^2/(1-z): Fser := series(F, z = 0, 38): seq(coeff(Fser, z, n), n = 0 .. 35);

CROSSREFS

Cf. A098071, A004148m A089735.

Sequence in context: A293313 A267539 A243722 * A243723 A243724 A243725

Adjacent sequences:  A187257 A187258 A187259 * A187261 A187262 A187263

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 05 2011

STATUS

approved

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)