A121123 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition).

1, 3, 12, 63, 342, 1998, 11772, 70308, 420552, 2521368, 15120432, 90710928, 544218912, 3265243488, 19591180992, 117546666048, 705278316672, 4231667380608, 25389994205952, 152339950119168, 914039640248832, 5484237750793728, 32905426141965312, 197432556307596288

Offset

2,2

Links

Table of n, a(n) for n=2..25.

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=0.

Index entries for linear recurrences with constant coefficients, signature (6,6,-36).

Formula

From Colin Barker, Aug 30 2013: (Start)

a(n) = 6*a(n-1)+6*a(n-2)-36*a(n-3) for n>5.

G.f.: x^2 -3*x^3*(-1+2*x+9*x^2) / ( (6*x-1)*(6*x^2-1) ). (End)

a(n) = A026532(n+1)/12 +6^(n-2)/4, n>2. - 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, I_m
A121123 := proc(r::integer)
    local q, a, f ;
    q := 9 ;
    a := 0 ;
    f := 1 +(-1)^(r+a) +(1+(-1)^a) *(1-(-1)^r) *floor((q-3)/2) /2 ;
    Jra(r, a, q)+binomial(2, r-a)+f*Hra(floor(r/2), floor(a/2), q) ;
    %/4 ;
end proc:
seq(A121123(n), n=2..30) ; # R. J. Mathar, Aug 01 2019

Mathematica

Join[{1}, LinearRecurrence[{6, 6, -36}, {3, 12, 63}, 23]] (* Jean-François Alcover, Mar 31 2020 *)

Crossrefs

Sequence in context: A266329 A208734 A305536 * A361882 A020123 A307708

Adjacent sequences: A121120 A121121 A121122 * A121124 A121125 A121126

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 13 2006

Status

approved