OFFSET
0,5
COMMENTS
Number of Dyck n-paths with at least one UUU. - David Scambler, Sep 17 2012
FORMULA
Conjecture: -(n+1)*(n-3)*(n+2)^2*a(n) +3*(n+1)*(2*n^3-n^2-15*n+8)*a(n-1) -(n-1)*(5*n^3-41*n+48)*a(n-2) -6*(n-1)*(n-2)*(2*n-5)*(n+3)*a(n-3)=0, n>=6 - R. J. Mathar, Mar 04 2018
MAPLE
MATHEMATICA
MotzkinNumber = DifferenceRoot[Function[{y, n}, {(-3n-3)*y[n] + (-2n-5)*y[n+1] + (n+4)*y[n+2] == 0, y[0] == 1, y[1] == 1}]];
a[n_] := CatalanNumber[n] - MotzkinNumber[n];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Oct 27 2021 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 20 2008
STATUS
approved