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A088518
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Symmetric secondary structures of RNA molecules with n nucleotides.
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3
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1, 1, 1, 2, 2, 4, 5, 9, 12, 21, 29, 50, 71, 121, 175, 296, 434, 730, 1082, 1812, 2709, 4521, 6807, 11328, 17157, 28485, 43359, 71844, 109830, 181674, 278769, 460443, 708840, 1169283, 1805291, 2974574, 4604363, 7578937, 11758552, 19337489, 30064037
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Diagonal sums of triangle in A088855. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 04 2009]
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FORMULA
| G.f. H(z) satisfies z^2*(1-z-z^2)H^2+(1-z-z^2)(1+z-z^2)H-(1+z-z^2)=0. H=[1/(1-z-z^2)]C(-z^2/(1-3z^2+z^4)), where C(z)=(1-sqrt(1-4z))/(2z) is the Catalan function. a(0)=a(1)=1; a(2n)=a(2n-1)+a(2n-2)-A004148(n-1) for n > 0; a(2n+1)=a(2n)+a(2n-1) for n > 0.
a(n) = F(n) - Sum[A004148(i)*F(n-1-2i), i=1..floor(n/2)-1], where F(i)=A000045(i) are the Fibonacci numbers. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 19 2003
a(n) is asymptotic to c*phi^n/sqrt(n) where phi=(1+sqrt(5))/2 and c=0.86.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 19 2003
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CROSSREFS
| Cf. A004148.
Sequence in context: A038000 A204856 A124280 * A001224 A102526 A050192
Adjacent sequences: A088515 A088516 A088517 * A088519 A088520 A088521
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2003
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