OFFSET
0,3
COMMENTS
a(n) = A162984(n,0).
LINKS
Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.
FORMULA
G.f. = G(z) satisfies G = 1 + zG + z^2*G + z^3*G(G-1).
D-finite with recurrence (n+3)*a(n) +(-2*n-3)*a(n-1) -n*a(n-2) +(-n+3)*a(n-4) +(-2*n+9)*a(n-5) +(n-6)*a(n-6)=0. - R. J. Mathar, Jul 22 2022
EXAMPLE
a(3)=3 because we have UDUDUD, UDUUDD, and UUDDUD.
MAPLE
G := ((1-z-z^2+z^3-sqrt(1-2*z-z^2-z^4-2*z^5+z^6))*1/2)/z^3: Gser := series(G, z = 0, 36): seq(coeff(Gser, z, n), n = 0 .. 31);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 11 2009
STATUS
approved