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A187259 Number of UH^jU's, DH^jD's, and DH^jU'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). 1
0, 0, 0, 0, 0, 0, 2, 11, 39, 122, 358, 1008, 2770, 7493, 20049, 53239, 140603, 369837, 969883, 2537685, 6628215, 17288950, 45048932, 117285552, 305159262, 793581817, 2062948149, 5361112383, 13929080271, 36183941553, 93984332531, 244094334682, 633922350198, 1646271999611 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n)=Sum(k*A098056(n,k), k>=0).

LINKS

Table of n, a(n) for n=0..33.

FORMULA

G.f.=z^5*G^2*(3G-1)(G-1)/[(1-z)(1-z^2*G^2)], where G=1+zG+z^2*G(G-1).

MAPLE

eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): gser := series(z^5*g^2*(3*g-1)*(g-1)/((1-z)*(1-z^2*g^2)), z = 0, 38): seq(coeff(gser, z, n), n = 0 .. 33);

CROSSREFS

Cf. A098056, A004148

Sequence in context: A259658 A000175 A276659 * A296593 A125064 A274326

Adjacent sequences:  A187256 A187257 A187258 * A187260 A187261 A187262

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 05 2011

STATUS

approved

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Last modified May 9 06:29 EDT 2021. Contains 343692 sequences. (Running on oeis4.)