OFFSET
0,3
LINKS
Helmut Prodinger, Dispersed Dyck paths revisited, arXiv:2402.13026 [math.CO], 2024.
FORMULA
a(n) = A191793(n,0).
G.f.: g(z) = 2/(1-2*z+z^4+sqrt(1-4*z^2+2*z^4+z^8)).
D-finite with recurrence (n+1)*a(n) +2*(-1)*a(n-1) +4*(-n+1)*a(n-2) +2*(n-3)*a(n-4) +6*a(n-5) +(n-7)*a(n-8)=0. - R. J. Mathar, Jul 22 2022
EXAMPLE
a(4)=5 because we have UDUU, UDUD, UUDU, UUUD, and UUUU, where U=(1,1) and D=(1,-1) (the path UUDD does not qualify).
MAPLE
g := 2/(1-2*z+z^4+sqrt(1-4*z^2+2*z^4+z^8)): gser := series(g, z = 0, 42): seq(coeff(gser, z, n), n = 0 .. 37);
MATHEMATICA
CoefficientList[Series[2/(1-2x+x^4+Sqrt[1-4x^2+2x^4+x^8]), {x, 0, 40}], x] (* Harvey P. Dale, Jun 19 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 18 2011
STATUS
approved