OFFSET
1,3
LINKS
Shu-Chung Liu, Jun Ma, Yeong-Nan Yeh, Dyck Paths with Peak- and Valley-Avoiding Sets, Stud. Appl Math. 121 (3) (2008) 263-289.
FORMULA
G.f.: (1 + x - 2*x^2 - sqrt(1 - 2*x - 3*x^2 + 4*x^4))/(2 - 2*x). - amended by Georg Fischer, Apr 09 2020
Conjecture: n*a(n) + 2*(1-n)*a(n-1) + (10-3*n)*a(n-2) + 4*a(n-3) + 4*(n-5)*a(n-4) = 0. - R. J. Mathar, Aug 14 2012
G.f.: 1 - 1/G(0) where G(k) = 1 - 1/(x + x^2/(1 + x/G(k+1) )); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 28 2012
MATHEMATICA
Rest[CoefficientList[Series[(1+x-2x^2-Sqrt[1-2x-3x^2+4x^4])/(2-2x), {x, 0, 30}], x]] (* Harvey P. Dale, Apr 10 2012; modified by Georg Fischer, Apr 09 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jun Ma (majun(AT)math.sinica.edu.tw), Nov 27 2008
STATUS
approved