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
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Aug 22 2006
EXTENSIONS
More terms from R. J. Mathar, Mar 18 2009
STATUS
approved