OFFSET
0,3
COMMENTS
a(n) is the number of lattice paths of n up steps and n down steps that start at the origin with an up step and do not cross the x-axis except possibly at (2n-2,0). - David Callan, Mar 14 2004
a(n) is the number of parking functions of size n avoiding the patterns 132, 213, 231, and 321. - Lara Pudwell, Apr 10 2023
LINKS
Ayomikun Adeniran and Lara Pudwell, Pattern avoidance in parking functions, Enumer. Comb. Appl. 3:3 (2023), Article S2R17.
FORMULA
D-finite with recurrence (n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-2*n+5)*a(n-2)=0, n>=3 - R. J. Mathar, Aug 25 2013
MATHEMATICA
Join[{1, 1}, Total/@Partition[CatalanNumber[Range[30]], 2, 1]] (* Harvey P. Dale, Mar 23 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 06 2002
STATUS
approved