|
|
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
|
|
|
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
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:
|
|
MATHEMATICA
|
Join[{1, 4, 19}, LinearRecurrence[{18, -96, 0, 1260, -1944, -3888, 7776}, {123, 834, 5796, 40014, 274590, 1867320, 12600360}, 20]] (* Jean-François Alcover, Apr 04 2020 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|