OFFSET
0,2
COMMENTS
This corrects a typographical error in A005497(6).
LINKS
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.
W. G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. [Annotated scanned copy]
Jean-François Alcover, Mathematica program
MAPLE
BrownE := proc(r, n, m)
local j, s, p ;
if r < 1 then
return 0 ;
elif r = 1 then
return A146305(n, m) ;
elif r = 2 then
j := n mod 2 ; s := floor(n/2) ;
if type(m, 'even') then
return 0 ;
end if;
p := (m+1)/2 ;
if p > 0 and s >= 0 then
return 2*(2*p)!*(4*s+2*p+2*j-1)!/p!/(p-1)!/s!/(3*s+2*p+2*j)! ;
else
return 0 ;
end if;
elif r =3 and (n mod 3) =0 and (m mod 3) = 0 then
s := n/3 ; p := m/3 ;
if p >= 0 and s >= 0 then
return (2*p+1)!*(4*s+2*p)!/p!/p!/s!/(3*s+2*p+1)! ;
else
return 0 ;
end if;
elif r >= 3 then
if ((n-1) mod r) =0 and ((m+3) mod r) =0 then
s := (n-1)/r ; p := (m+3)/r-1 ;
if p>=0 and s>=0 then
return (2*p+2)!*(4*s+2*p+1)!/p!/(p+1)!/s!/(3*s+2*p+2)! ;
else
return 0 ;
end if;
else
return 0 ;
end if;
else
return 0 ;
end if;
end proc:
BrownG := proc(n, m)
add( numtheory[phi](s)* BrownE(s, n, m), s = numtheory[divisors](m+3) ) ;
%/(m+3) ;
end proc:
A210696 := proc(n)
BrownG(1, n) ;
end proc:
seq(A210696(n), n=0..25) ;
MATHEMATICA
See the link section.
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Mar 30 2012
STATUS
approved