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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.
2
1, 10, 160, 3200, 72960, 1813504, 47923200, 1325629440, 37991219200, 1120005652480, 33789432561664, 1039157228994560, 32480974549811200, 1029463445864448000, 33023079530417356800, 1070513886720329515008, 35026358912891580579840, 1155516042520241436098560
OFFSET
1,2
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Dec 01 2003
EXTENSIONS
More terms from Michel Marcus, Dec 11 2014
STATUS
approved