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A121125 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition). 1
1, 4, 19, 123, 834, 5796, 40014, 274590, 1867320, 12600360, 84407832, 561852936, 3718716480, 24488941248, 160538000544, 1048121604576, 6817684235904, 44197394428800, 285637390727040, 1840774252406400, 11831735032492032, 75865287873171456, 485355033432322560 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..24.

J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 12 q=9 alpha=2.

Index entries for linear recurrences with constant coefficients, signature (18,-96,0,1260,-1944,-3888,7776).

FORMULA

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

MAPLE

# Exhibit 1

Hra := proc(r::integer, a::integer, q::integer)

    binomial(r-1, a-1)*(q-3)+binomial(r-1, a) ;

    %*(q-3)^(r-a-1) ;

end proc:

Jra := proc(r::integer, a::integer, q::integer)

    binomial(r-2, a-2)*(q-3)^2 +2*binomial(r-2, a-1)*(q-3) +binomial(r-2, a) ;

    %*(q-3)^(r-a-2) ;

end proc:

# Exhibit 2

A121125 := proc(r::integer)

    q := 9 ;

    a := 2 ;

    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) ;

    %/4 ;

end proc:

seq(A121125(n), n=2..30) ; # R. J. Mathar, Aug 01 2019

MATHEMATICA

Join[{1, 4, 19}, LinearRecurrence[{18, -96, 0, 1260, -1944, -3888, 7776}, {123, 834, 5796, 40014, 274590, 1867320, 12600360}, 20]] (* Jean-Fran├žois Alcover, Apr 04 2020 *)

CROSSREFS

Sequence in context: A197660 A094822 A280939 * A099953 A009324 A203236

Adjacent sequences:  A121122 A121123 A121124 * A121126 A121127 A121128

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 13 2006

STATUS

approved

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Last modified September 23 00:32 EDT 2021. Contains 347609 sequences. (Running on oeis4.)