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Search: id:A092387
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| A092387 |
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Fibonacci(2*n+1)+fibonacci(2*n-1)+2. |
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+0
1
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| 5, 9, 20, 49, 125, 324, 845, 2209, 5780, 15129, 39605, 103684, 271445, 710649, 1860500, 4870849, 12752045, 33385284, 87403805, 228826129, 599074580, 1568397609, 4106118245, 10749957124, 28143753125, 73681302249, 192900153620
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Let b(k)=sum(i=1,k,F(2*n*i)*binomial(k,i)) where F(k) denotes the k-th Fibonacci number. The (b(k)) sequence satisfies the recursion: b(k)=a(n)*(b(k-1)-b(k-2)).
Same as the number of Kekule structures in polyphenanthrene in terms of the number of hexagons. - Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Aug 22 2006
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REFERENCES
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I. Lukovits and D. Janezic, "Enumeration of conjugated circuits in nanotubes", J. Chem. Inf. Comput. Sci., vol. 44 (2004) pp. 410-414. See Table 1 column 3 on page 411.
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FORMULA
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a(1)=5, a(2)=9, a(3)=20, a(n)=4*a(n-1)-4*a(n-2)+a(n-3); a(n)=3+floor((1+phi)^n) where phi=(1+sqrt(5))/2; a(n)=A005248(n)+2
G.f.: -x*(5-11*x+4*x^2)/((x-1)(x^2-3*x+1)). a(n+1)-a(n)=A002878(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009]
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CROSSREFS
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Equals A065034(n)+1.
Sequence in context: A102172 A011983 A087940 this_sequence A160720 A147552 A147562
Adjacent sequences: A092384 A092385 A092386 this_sequence A092388 A092389 A092390
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 20 2004
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EXTENSIONS
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Better definition from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 20 2004
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