cp's OEIS Frontend

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.

%I A090374 #21 Mar 29 2023 07:40:27
%S A090374 1,10,160,3200,72960,1813504,47923200,1325629440,37991219200,
%T A090374 1120005652480,33789432561664,1039157228994560,32480974549811200,
%U A090374 1029463445864448000,33023079530417356800,1070513886720329515008,35026358912891580579840,1155516042520241436098560
%N 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.
%H A090374 M. Bousquet-Mélou and G. Schaeffer, <a href="http://dx.doi.org/10.1006/aama.1999.0673">Enumeration of planar constellations</a>, Adv. in Appl. Math. v.24 (2000), 337-368.
%F A090374 a(n) = 5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2)). - corrected by _Michel Marcus_, Dec 11 2014
%F A090374 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
%p A090374 A090374 := proc(n)
%p A090374     5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2))
%p A090374 end proc:
%p A090374 seq(A090374(n),n=1..40) ; # _R. J. Mathar_, Mar 29 2023
%t A090374 a[n_] := 5 2^(2n) (4n-1)! / ((n-1)! (3n+2)!);
%t A090374 Array[a, 18] (* _Jean-François Alcover_, Aug 28 2019 *)
%o A090374 (PARI) vector(20, n, 5*4^(n-1)*binomial(4*n, n)/((3*n+1)*(3*n+2))) \\ _Michel Marcus_, Dec 11 2014
%Y A090374 Cf. A000257, A069726, A069729, A090373.
%K A090374 easy,nonn
%O A090374 1,2
%A A090374 _Valery A. Liskovets_, Dec 01 2003
%E A090374 More terms from _Michel Marcus_, Dec 11 2014