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

1,2

Links

Table of n, a(n) for n=1..18.

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-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

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 *)

Prog

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

Crossrefs

Cf. A000257, A069726, A069729, A090373.

Sequence in context: A106261 A112125 A366037 * A034724 A234283 A074703

Adjacent sequences: A090371 A090372 A090373 * A090375 A090376 A090377

Keyword

easy,nonn

Author

Valery A. Liskovets, Dec 01 2003

Extensions

More terms from Michel Marcus, Dec 11 2014

Status

approved