OFFSET
0,4
COMMENTS
a(n) is the number of Dyck paths of length n without the height of peaks 2 (mod 3) and the height of valleys 1 (mod 3)
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..2028
Jean-Luc Baril, Rigoberto Flórez, and José L. Ramírez, Counting symmetric and asymmetric peaks in motzkin paths with air pockets, Univ. Bourgogne (France, 2023).
FORMULA
D-finite with recurrence: (n+1)*a(n) +(-5*n+1)*a(n-1) +9*(n-1)*a(n-2) +12*(-n+2)*a(n-3) +2*(4*n-11)*a(n-4) +2*(-2*n+7)*a(n-5)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-4x+4x^2-4x^3])/(2(1-x+x^2)x), {x, 0, 40}], x] (* Harvey P. Dale, Feb 07 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jun Ma (majun(AT)math.sinica.edu.tw), Nov 27 2008
EXTENSIONS
Offset corrected. - R. J. Mathar, Jan 25 2020
STATUS
approved