A090374 Number of rooted planar 4-constellations with n quadrangles: rooted planar maps with bicolored faces having n black quadrangular faces and an arbitrary number of white faces of degrees multiple to 4.

1, 10, 160, 3200, 72960, 1813504, 47923200, 1325629440, 37991219200, 1120005652480, 33789432561664, 1039157228994560, 32480974549811200, 1029463445864448000, 33023079530417356800, 1070513886720329515008, 35026358912891580579840, 1155516042520241436098560

Offset: 1

Author

Valery A. Liskovets, Dec 01 2003

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A000257, A069726, A069729, A090373.

Programs

Maple

A090374 := proc(n)
    5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2))
end proc:
seq(A090374(n),n=1..40) ; # R. J. Mathar, Mar 29 2023

Mathematica

a[n_] := 5 2^(2n) (4n-1)! / ((n-1)! (3n+2)!);
Array[a, 18] (* Jean-François Alcover, Aug 28 2019 *)

PARI

vector(20, n, 5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2))) \\ Michel Marcus, Dec 11 2014

Formula

a(n) = 5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2)). - corrected by Michel Marcus, Dec 11 2014

D-finite with recurrence 3*n*(3*n+2)*(3*n+1)*a(n) -32*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Mar 29 2023

Extensions

More terms from Michel Marcus, Dec 11 2014