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

1,4

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

Table of n, a(n) for n=1..27.

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

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

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 *)

Crossrefs

Cf. A056487.

Sequence in context: A155119 A370234 A114169 * A307526 A067411 A045915

Adjacent sequences: A121099 A121100 A121101 * A121103 A121104 A121105

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 11 2006

Status

approved