OFFSET
2,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 13 2006
STATUS
approved