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A244886
G.f.: (1-x+sqrt(1-2*x-3*x^2))/(1-3*x+x^2+x^3+(1-x^2)*sqrt(1-2*x-3*x^2)).
2
1, 1, 2, 4, 9, 22, 56, 147, 393, 1065, 2915, 8042, 22330, 62339, 174837, 492313, 1391134, 3943130, 11207594, 31934552, 91197474, 260969372, 748176873, 2148622932, 6180146228, 17801978083, 51347929943, 148293450023, 428774359142, 1241110916678
OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)
J.-L. Baril and A. Petrossian, Equivalence classes of Dyck paths modulo some statistics, Discrete Mathematics, Volume 338, Issue 4, 6 April 2015, Pages 655-660. See Theorem 1.
Jean-Luc Baril, José L. Ramírez, and Lina M. Simbaqueba, Equivalence Classes of Skew Dyck Paths Modulo some Patterns, 2021.
K. Manes, A. Sapounakis, I. Tasoulas, and P. Tsikouras, Equivalence classes of ballot paths modulo strings of length 2 and 3, arXiv:1510.01952 [math.CO], 2015.
FORMULA
a(n) ~ 3^(n+7/2)/(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 10 2014
Conjecture D-finite with recurrence: n*a(n) +(-5*n+3)*a(n-1) +2*(n)*a(n-2) +(13*n-30)*a(n-3) +3*(-1)*a(n-4) +(-8*n+21)*a(n-5) +3*(-n+3)*a(n-6)=0. - R. J. Mathar, Jan 24 2020
MATHEMATICA
CoefficientList[Series[(1 - x + Sqrt[1 - 2 x - 3 x^2])/(1 - 3 x + x^2 + x^3 + (1 - x^2) Sqrt[1 - 2 x - 3 x^2]), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2014 *)
PROG
(PARI) my(x='x+O('x^50)); Vec((1-x+sqrt(1-2*x-3*x^2))/(1-3*x+x^2+x^3+(1-x^2)*sqrt(1-2*x-3*x^2))) \\ G. C. Greubel, Apr 05 2017
CROSSREFS
Sequence in context: A025265 A152225 A037245 * A143017 A307575 A301362
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 09 2014
STATUS
approved