login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097107 Triangle read by rows: T(n,k) = number of peakless Motzkin paths of length n and containing a total of k level steps H in all DHH...HU's, where U=(1,1), H=(1,0) and D=(1,-1) (can be easily expressed using RNA secondary structure terminology). 0
1, 1, 1, 2, 4, 8, 17, 36, 1, 77, 4, 1, 167, 13, 4, 1, 365, 40, 13, 4, 1, 805, 114, 41, 13, 4, 1, 1790, 314, 119, 42, 13, 4, 1, 4008, 845, 335, 124, 43, 13, 4, 1, 9033, 2230, 925, 356, 129, 44, 13, 4, 1, 20477, 5809, 2506, 1006, 377, 134, 45, 13, 4, 1, 46663, 14980, 6712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums yield the RNA secondary structure numbers (A004148).

LINKS

Table of n, a(n) for n=0..63.

I. L. Hofacker, P. Schuster and P. F. Stadler, Combinatorics of RNA secondary structures, Discrete Appl. Math., 88, 1998, 207-237.

P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26 (1979), 261-272.

M. Vauchassade de Chaumont and G. Viennot, Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Sem. Loth. Comb. B08l (1984) 79-86. [Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, p. 79-86.]

FORMULA

G.f.: G=G(t, z) satisfies G=1+zG+z^2*(G-1)[(1-z)G+z(1-t)/(1-z)]/(1-tz).

EXAMPLE

Triangle starts:

1;

1;

1;

2;

4;

8;

17;

36,1;

77,4,1;

167,13,4,1;

Row n>=6 contains n-5 terms.

T(10,3)=4 because we have UHD(HHH)UHDH, UHD(HHH)UHHD, HUHD(HHH)UHD and UHHD(HHH)UHD, where U=(1,1), H=(1,0) and D=(1,-1); the 3 required H's are shown between parentheses.

CROSSREFS

Cf. A004148.

Sequence in context: A127680 A136750 A274115 * A098083 A182900 A202843

Adjacent sequences:  A097104 A097105 A097106 * A097108 A097109 A097110

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Sep 16 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 3 16:55 EDT 2022. Contains 357237 sequences. (Running on oeis4.)