A121257 Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units.
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
Offset: 1
Keywords
Examples
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.
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).
Programs
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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
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
Extensions
More terms from R. J. Mathar, Mar 18 2009
Comments