

A090374


Number of rooted planar 4constellations 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



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

1,2


LINKS

Table of n, a(n) for n=1..18.
M. BousquetMélou and G. Schaeffer, Enumeration of planar constellations, Adv. in Appl. Math. v.24 (2000), 337368.


FORMULA

a(n) = 5*4^(n1)*binomial(4*n, n)/((3*n+1)*(3*n+2)).  corrected by Michel Marcus, Dec 11 2014


MATHEMATICA

a[n_] := 5 2^(2n) (4n1)! / ((n1)! (3n+2)!);
Array[a, 18] (* JeanFrançois Alcover, Aug 28 2019 *)


PROG

(PARI) vector(20, n, 5*4^(n1)*binomial(4*n, n)/((3*n+1)*(3*n+2))) \\ Michel Marcus, Dec 11 2014


CROSSREFS

Cf. A000257, A069726, A069729, A090373.
Sequence in context: A180881 A106261 A112125 * 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



