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A187258 Number of UH^jD's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology). 0
0, 0, 0, 1, 3, 7, 17, 41, 99, 242, 596, 1477, 3681, 9215, 23155, 58368, 147530, 373768, 948882, 2413264, 6147414, 15682008, 40056238, 102434119, 262228051, 671945055, 1723350315, 4423518544, 11362907022, 29208834520, 75131251334, 193370093508, 497969663062 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)=Sum(k*A089741(n,k), k>=0).

LINKS

Table of n, a(n) for n=0..32.

FORMULA

G.f.=z^3*G^2/[(1-z)(1-z^2*G^2)], where G=1+zG+z^2*G(G-1).

EXAMPLE

a(4)=3 because in HHHH, HUHD, UHDH, and UHHD we have 0+1+1+1 subwords of the type UH^jD.

MAPLE

eq := g = 1+z*g+z^2*g*(g-1): G := RootOf(eq, g): Gser := series(z^3*G^2/((1-z)*(1-z^2*G^2)), z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 32);

CROSSREFS

Cf. A089741, A004148

Sequence in context: A123335 A078057 A089742 * A131721 A259855 A058351

Adjacent sequences:  A187255 A187256 A187257 * A187259 A187260 A187261

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 05 2011

STATUS

approved

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Last modified February 18 04:10 EST 2018. Contains 299298 sequences. (Running on oeis4.)