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A187254 Number of 3-noncrossing RNA structures over 2n vertices with no isolated vertices. 1
1, 0, 1, 4, 22, 139, 979, 7484, 61018, 523995, 4696277, 43623618, 417729564, 4106089683, 41289287337, 423556384020, 4422308778458, 46904447607369, 504544306691569, 5496706186024364, 60576765646658782, 674624324569952719, 7585425185883023881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n)=A187253(2n,0).

REFERENCES

Emma Y. Jin, Jing Qin and Christian M. Reidys, "Combinatorics of RNA structures with pseudoknots", Bulletin of Mathematical Biology Vol. 70 (2008) pp. 45-67.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n)=Sum((-1)^j*binom(2n-j,j)*[c(n-j)c(n-j+2) - c(n-j+1)^2], j=0..n), where c(i)=A000108(i) are the Catalan numbers.

EXAMPLE

a(3)=4 because we have ABACBC, ABCBAC, ABCACB, and ABCBCA, where identically labeled vertices are assumed to be joined by an arc.

MAPLE

c := proc (n) options operator, arrow: binomial(2*n, n)/(n+1) end proc: a := proc (n) options operator, arrow: sum((-1)^j*binomial(2*n-j, j)*(c(n-j)*c(n-j+2)-c(n-j+1)^2), j = 0 .. n) end proc: seq(a(n), n = 0 .. 22);

CROSSREFS

Cf. A187253

Sequence in context: A025756 A200731 A193116 * A216712 A240586 A002293

Adjacent sequences:  A187251 A187252 A187253 * A187255 A187256 A187257

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 24 2011

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)