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Search: id:A121257
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| A121257 |
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Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units. |
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+0
1
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| 4, 20, 76, 260, 840, 2616, 7940, 23644, 69380, 201220, 578064, 1647600, 4664836, 13132580, 36789820, 102621956, 285174360, 789810984, 2180889860, 6005842540, 16498958324, 45225010180, 123715684896, 337806904800, 920819997700
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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See Table 2 on page 412 of Lukovits and Janezic paper for details.
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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.
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FORMULA
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a(n)= 6a(n-1)-11a(n-2)+6a(n-3)-a(n-4)=4*A001870(n-1). G.f.: -4*x*(-1+x)/(x^2-3*x+1)^2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009]
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EXAMPLE
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If n=5 then the number of conjugated cycles composed of six carbons in (1,1)-nanotubes is 840 which is the fifth term in the sequence. Here n is the number of naphthalene units.
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MAPLE
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Kn11 := proc(n) if n <= 0 then n+2 ; else 3*procname(n-1)-procname(n-2) ; fi; end: Ksub11 := proc(n) if n = -1 then 1 ; elif n = 0 then 3 ; else Kn11(n)+procname(n-1) ; fi; end: a := proc(n) 4*add( Ksub11(j)*Kn11(n-3-j), j=-1..n-2) ; end: seq(a(n), n=0..20) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009]
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CROSSREFS
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Sequence in context: A006740 A061981 A054611 this_sequence A145563 A125669 A082138
Adjacent sequences: A121254 A121255 A121256 this_sequence A121258 A121259 A121260
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KEYWORD
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nonn
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Aug 22 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009
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