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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
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).
Conjecture D-finite with recurrence -(n+1)*(42968*n-187991)*a(n) +(-33354*n^2+888062*n+187991)*a(n-1) +(587317*n^2-5596253*n+61483
17)*a(n-2) +(-549823*n^2+5720814*n-11020859)*a(n-3) +(176865*n^2-2521427*n+8169148)*a(n-4) +(-587317*n^2+6446371*n-18005842)*a(n-5)
+(592791*n^2-6850333*n+19290494)*a(n-6) -(143511*n-619655)*(n-8)*a(n-7)=0. - R. J. Mathar, Jul 22 2022
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
Sequence in context: A350952 A000175 A276659 * A296593 A125064 A361493
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 05 2011
STATUS
approved

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Last modified March 19 06:56 EDT 2024. Contains 370953 sequences. (Running on oeis4.)