%I #13 Apr 04 2020 10:30:19

%S 1,4,19,123,834,5796,40014,274590,1867320,12600360,84407832,561852936,

%T 3718716480,24488941248,160538000544,1048121604576,6817684235904,

%U 44197394428800,285637390727040,1840774252406400,11831735032492032,75865287873171456,485355033432322560

%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=2.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (18,-96,0,1260,-1944,-3888,7776).

%F G.f. x^2 +4*x^3 +19*x^4 -3*x^5*(41 -460*x +864*x^2 +5250*x^3 -14742*x^4 -15228*x^5 +48600*x^6) / ( (6*x^2-1)^2*(6*x-1)^3 ). - _R. J. Mathar_, Aug 01 2019

%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 A121125 := proc(r::integer)

%p q := 9 ;

%p a := 2 ;

%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(A121125(n),n=2..30) ; # _R. J. Mathar_, Aug 01 2019

%t Join[{1, 4, 19}, LinearRecurrence[{18, -96, 0, 1260, -1944, -3888, 7776}, {123, 834, 5796, 40014, 274590, 1867320, 12600360}, 20]] (* _Jean-François Alcover_, Apr 04 2020 *)

%K nonn,easy

%O 2,2

%A _N. J. A. Sloane_, Aug 13 2006