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%I #8 Aug 12 2015 01:59:25
%S 4,20,76,260,840,2616,7940,23644,69380,201220,578064,1647600,4664836,
%T 13132580,36789820,102621956,285174360,789810984,2180889860,
%U 6005842540,16498958324,45225010180,123715684896,337806904800,920819997700
%N Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units.
%C See Table 2 on page 412 of Lukovits and Janezic paper for details.
%D I. Lukovits and D. Janezic, "Enumeration of conjugated circuits in nanotubes", J. Chem. Inf. Comput. Sci., vol. 44 (2004) pp. 410-414.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6, -11, 6, -1).
%F 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
%e 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.
%p 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
%K nonn
%O 1,1
%A _Parthasarathy Nambi_, Aug 22 2006
%E More terms from _R. J. Mathar_, Mar 18 2009
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