login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A090373 Number of unrooted planar 4-constellations with n quadrangles. 2
1, 10, 60, 875, 14600, 303814, 6846180, 165740155, 4221248540, 112001557620, 3071766596524, 86596464513410, 2498536503831640, 73533104142072810, 2201538635362482480, 66907117946947479163, 2060374053699504740000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are planar maps with bicolored faces having n black quadrangular faces and an arbitrary number of white faces of degrees multiple to 4. The vertices can be and are colored so that any black quadrangle is colored counterclockwise 1,2,3,4. Isomorphisms are required to respect the colorings.

LINKS

Table of n, a(n) for n=1..17.

M. Bousquet-Mélou and G. Schaeffer, Enumeration of planar constellations, Adv. in Appl. Math. v.24 (2000), 337-368.

FORMULA

a(n) = (5/(4*n))*(4^n*binomial(4*n,n)/((3*n+1)*(3*n+2))+s/2) where s = -4^n* binomial(4*n,n) + Sum_{d|n} (phi(n/d)*4^d*binomial(4*d,d)). - Jean-François Alcover, Aug 29 2019

MAPLE

with(numtheory): C_4 := proc(n) local s, d; if n=0 then RETURN(1) else s := -4^n*binomial(4*n, n); for d in divisors(n) do s := s+phi(n/d)*4^d*binomial(4*d, d) od; RETURN((5/(4*n))*(4^n*binomial(4*n, n)/((3*n+1)*(3*n+2))+s/2)); fi; end;

MATHEMATICA

a[n_] := Module[{s}, s = -4^n Binomial[4n, n]; Do[s += EulerPhi[n/d] 4^d Binomial[4d, d], {d, Divisors[n]}]; (5/(4n))(4^n Binomial[4n, n]/((3n+1)(3n+2)) + s/2)];

Array[a, 17] (* Jean-François Alcover, Aug 29 2019 *)

CROSSREFS

Cf. A090372, A090374.

Sequence in context: A281863 A219368 A052664 * A218427 A041184 A089034

Adjacent sequences:  A090370 A090371 A090372 * A090374 A090375 A090376

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Dec 01 2003

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 July 2 16:14 EDT 2020. Contains 335404 sequences. (Running on oeis4.)