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

1,1

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

Table of n, a(n) for n=1..25.

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