login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046650 Number of rooted planar maps. 1
1, 1, 2, 4, 14, 49, 216, 984, 4862, 24739, 130338, 701584, 3852744, 21489836, 121525520, 695307888, 4019381790, 23446201495, 137875564710, 816646459860, 4868578092510, 29196022525905, 176022392938080, 1066433501134560, 6490009570139784, 39659537885087124, 243278423033093336, 1497584057249141728, 9249144367260811824 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Table III with row sums A000087 is (A046653 row-reversed)

1,

1,1,

2,1,1,

4,3,2,1,

14,12,8,2,1,

49,43,30,12,3,1,

216,189,134,63,22,3,1,

984,888,608,323,133,31,4,1,

4862,4332,2988,1671,759,238,48,4,1,

# R. J. Mathar, Apr 13 2019

LINKS

Table of n, a(n) for n=2..30.

W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.

FORMULA

Reference gives generating functions.

MAPLE

B1nm := proc(n, m) # eq (4.15)

    local j ;

    if m>=2 and n>= m  then

        add((3*m-2*j-1)*(2*j-m)*(j-2)!*(3*n-j-m-1)!/(n-j)!/(j-m)!/(j-m+1)!/(2*m-j)!, j=m..min(n, 2*m) ) ;

        %*m/(2*n-m)! ;

    else

        0 ;

    end if;

end proc:

B2wj := proc(w, j) # eq (8.21)

    local k ;

    if  w >= j and j>=1 and w >= 1 then

        add((2*k-j+1)*(k-1)!*(3*w-k-j)!/(k-j+1)!/(k-j)!/(2*j-k-1)!/(w-k)!, k=j..min(w, 2*j-1) ) ;

        %*j/(2*w-j+1)! ;

    else

        0;

    end if;

end proc:

Brwj := proc(r, w, j) # eq. (8.21)

    local k ;

    if  w >= j and j>=1 and w>=1 and r > 1 then

        add((2*k-j)*(k-1)!*(3*w-k-j-1)!/((k-j)!)^2/(2*j-k)!/(w-k)!, k=j..min(w, 2*j) ) ;

        %*j/(2*w-j)! ;

    else

        0 ;

    end if;

end proc:

Brnm := proc(r, n, m)

    if r = 1 then

        B1nm(n, m) ;

    elif r = 2 and type(n, 'odd') and type (m, 'even') then

        B2wj((n-1)/2, m/2) ;

    elif modp(n, r) <> 0 or modp(m, r) <> 0 then

        0;

    else

        Brwj(r, n/r, m/r) ;

    end if;

end proc:

L := proc(n, m) # eq. (6.7)

    add(numtheory[phi](s)*Brnm(s, n, m), s=numtheory[divisors](m)) ;

    %/m ;

end proc:

seq(L(n, 2), n=2..40) ; # R. J. Mathar, Apr 13 2019

CROSSREFS

Cf. A000087.

Sequence in context: A032222 A212268 A092665 * A327235 A055727 A003500

Adjacent sequences:  A046647 A046648 A046649 * A046651 A046652 A046653

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from R. J. Mathar, Apr 13 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)