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 A121257 Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See Table 2 on page 412 of Lukovits and Janezic paper for details. REFERENCES I. Lukovits and D. Janezic, "Enumeration of conjugated circuits in nanotubes", J. Chem. Inf. Comput. Sci., vol. 44 (2004) pp. 410-414. LINKS Index entries for linear recurrences with constant coefficients, signature (6, -11, 6, -1). FORMULA 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. - R. J. Mathar, Mar 18 2009 EXAMPLE 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. MAPLE 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) ; # R. J. Mathar, Mar 18 2009 CROSSREFS Sequence in context: A196432 A302815 A196508 * A145563 A125669 A295116 Adjacent sequences:  A121254 A121255 A121256 * A121258 A121259 A121260 KEYWORD nonn AUTHOR Parthasarathy Nambi, Aug 22 2006 EXTENSIONS More terms from R. J. Mathar, Mar 18 2009 STATUS approved

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Last modified April 6 09:00 EDT 2020. Contains 333268 sequences. (Running on oeis4.)