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A121102 Catapolyoctagons (see Cyvin et al. for precise definition).

%I A121102 #16 Jun 07 2023 08:31:18
%S A121102 0,0,0,4,24,144,744,3844,19344,97344,487344,2439844,12202344,61027344,
%T A121102 305152344,1525839844,7629277344,38146777344,190734277344,
%U A121102 953673339844,4768368652344,23841853027344,119209274902344,596046423339844,2980232165527344,14901161071777344,74505805603027344
%N A121102 Catapolyoctagons (see Cyvin et al. for precise definition).
%D A121102 S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70, Table 1 Symmetry C_s.
%H A121102 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,-30,25).
%F A121102 From _R. J. Mathar_, Jul 31 2019: (Start)
%F A121102 G.f.: -4*x^4/((x - 1)*(5*x - 1)*(5*x^2 - 1)).
%F A121102 4*a(n) = 5^(n-2) + 1 - 10*A056487(n-4). (End)
%F A121102 E.g.f.: (25*cosh(x) + cosh(5*x) - 10*cosh(sqrt(5)*x) + 25*sinh(x) + sinh(5*x) - 6*sqrt(5)*sinh(sqrt(5)*x) - 16)/100. - _Stefano Spezia_, Jun 06 2023
%p A121102 A121102 := proc(n)
%p A121102     local mr,ar,cr,dr ,ir,p5;
%p A121102     if n = 1 then
%p A121102         ar := 1 ;
%p A121102     else
%p A121102         ar := 0 ;
%p A121102     end if;
%p A121102     dr := 1-ar ;
%p A121102     p5 := 5^(floor(n/2)-1) ;
%p A121102     if n = 1 then
%p A121102         cr :=0 ;
%p A121102     else
%p A121102         cr := (p5-1)/2+2*ar/5 ;
%p A121102     end if;
%p A121102     mr := (3-2*(-1)^n)*p5/2-1/2 ;
%p A121102     if n = 1 then
%p A121102         ir := 1;
%p A121102     else
%p A121102         ir := (5^(n-2)+1)/4  +(2-(-1)^n)*p5/2 -3*ar/5 ;
%p A121102     end if;
%p A121102     ir-ar-dr-cr-mr ;
%p A121102 end proc:
%p A121102 seq(A121102(n),n=1..30) ; # _R. J. Mathar_, Jul 31 2019
%t A121102 LinearRecurrence[{6, 0, -30, 25}, {0, 0, 0, 4}, 27] (* _Jean-François Alcover_, Mar 31 2020 *)
%Y A121102 Cf. A056487.
%K A121102 nonn,easy
%O A121102 1,4
%A A121102 _N. J. A. Sloane_, Aug 11 2006