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A176006
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The number of branching configurations of RNA (see Sankoff, 1985) with n or fewer hairpins.
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0
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1, 2, 4, 10, 32, 122, 516, 2322, 10880, 52466, 258564, 1296282, 6589728, 33887466, 175966212, 921353250, 4858956288, 25786112994, 137604139012, 737922992938, 3974647310112, 21493266631002, 116642921832964, 635074797251890
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..23.
Guo-Niu Han, Enumeration of Standard Puzzles
Sankoff (1985) Simultaneous solution of the RNA folding, alignment and protosequence problems, Siam J. Appl. Math 45(5):810-825.
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FORMULA
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G.f. (3-z-sqrt(1-6z+z^2))/(2(1-z)).
Conjecture : n*a(n) +(9-7*n)*a(n-1) +(7*n-12)*a(n-2) +(3-n)*a(n-3)=0. - R. J. Mathar, Jul 24 2012
a(n) ~ 2^(1/4)*(3+2*sqrt(2))^n/(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012
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EXAMPLE
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For n = 3, the a(3) = 10 branching configurations with 3 or fewer hairpins are: unfolded, (), ()(), (()()), ()()(), (()())(), ()(()()), (()()()), ((()())()), and (()(()())).
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MATHEMATICA
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CoefficientList[Series[(3-x-Sqrt[1-6*x+x^2])/(2*(1-x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
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CROSSREFS
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The cumulative sums of A155069.
Sequence in context: A071954 A120017 A000736 * A001250 A013032 A098830
Adjacent sequences: A176003 A176004 A176005 * A176007 A176008 A176009
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KEYWORD
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easy,nonn
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AUTHOR
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Lee A. Newberg, Apr 05 2010
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STATUS
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approved
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