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%I #15 Apr 04 2020 10:30:12
%S 1,4,21,138,864,5526,34992,221724,1399680,8818632,55427328,347684400,
%T 2176782336,13604912928,84894511104,528958247616,3291294892032,
%U 20453047668864,126949945835520,787089669219072,4874877920083968,30163307160752640,186464080443211776,1151689908801235968
%N Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition).
%H J. Brunvoll, S. J. Cyvin and B. N. Cyvin, <a href="https://doi.org/10.1016/0166-1280(95)04463-9">Isomer enumeration of polygonal systems...</a>, J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 12, q=9, alpha=1.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-30,-72,216).
%F From _R. J. Mathar_, Aug 01 2019: (Start)
%F G.f.: x^2 +4*x^3 -3*x^4*(7-38*x-54*x^2+270*x^3) / ( (6*x^2-1)*(-1+6*x)^2 ).
%F a(n) = A000400((n-1)/2)/12 +6^(n-1)/16 +A053469(n+1)/864, where Axxxxx(.) is zero for fractional indices, n>3. (End)
%p # Exhibit 1
%p Hra := proc(r::integer,a::integer,q::integer)
%p binomial(r-1,a-1)*(q-3)+binomial(r-1,a) ;
%p %*(q-3)^(r-a-1) ;
%p end proc:
%p Jra := proc(r::integer,a::integer,q::integer)
%p binomial(r-2,a-2)*(q-3)^2 +2*binomial(r-2,a-1)*(q-3) +binomial(r-2,a) ;
%p %*(q-3)^(r-a-2) ;
%p end proc:
%p # Exhibit 2
%p A121124 := proc(r::integer)
%p q := 9 ;
%p a := 1 ;
%p Jra(r,a,q)+binomial(2,r-a)+( 1 +(-1)^(r+a) +(1+(-1)^a)*(1-(-1)^r)*floor((q-3)/2)/2)*Hra(floor(r/2),floor(a/2),q) ;
%p %/4 ;
%p end proc:
%p seq(A121124(n),n=2..30) # _R. J. Mathar_, Aug 01 2019
%t Join[{1, 4}, LinearRecurrence[{12, -30, -72, 216}, {21, 138, 864, 5526}, 22]] (* _Jean-François Alcover_, Apr 04 2020 *)
%K nonn,easy
%O 2,2
%A _N. J. A. Sloane_, Aug 13 2006
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