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

0, 0, 0, 4, 24, 144, 744, 3844, 19344, 97344, 487344, 2439844, 12202344, 61027344, 305152344, 1525839844, 7629277344, 38146777344, 190734277344, 953673339844, 4768368652344, 23841853027344, 119209274902344, 596046423339844, 2980232165527344, 14901161071777344, 74505805603027344

Offset: 1

Author

N. J. A. Sloane, Aug 11 2006

Keywords

• nonn
• easy

References

• 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.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,0,-30,25).

Crossrefs

Cf. A056487.

Programs

Maple

A121102 := proc(n)
    local mr,ar,cr,dr ,ir,p5;
    if n = 1 then
        ar := 1 ;
    else
        ar := 0 ;
    end if;
    dr := 1-ar ;
    p5 := 5^(floor(n/2)-1) ;
    if n = 1 then
        cr :=0 ;
    else
        cr := (p5-1)/2+2*ar/5 ;
    end if;
    mr := (3-2*(-1)^n)*p5/2-1/2 ;
    if n = 1 then
        ir := 1;
    else
        ir := (5^(n-2)+1)/4  +(2-(-1)^n)*p5/2 -3*ar/5 ;
    end if;
    ir-ar-dr-cr-mr ;
end proc:
seq(A121102(n),n=1..30) ; # R. J. Mathar, Jul 31 2019

Mathematica

LinearRecurrence[{6, 0, -30, 25}, {0, 0, 0, 4}, 27] (* Jean-François Alcover, Mar 31 2020 *)

Formula

From R. J. Mathar, Jul 31 2019: (Start)

G.f.: -4*x^4/((x - 1)*(5*x - 1)*(5*x^2 - 1)).

4*a(n) = 5^(n-2) + 1 - 10*A056487(n-4). (End)

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