OFFSET
0,3
LINKS
Christian Bean, Antonio Bernini, Matteo Cervetti and Luca Ferrari, Pattern avoiding Motzkin paths are almost rational, arXiv:2108.03037 [math.CO], 2021.
FORMULA
G.f.: (1-3*x-4*x^2+12*x^3 - (1-3*x-4*x^2+8*x^3)*sqrt(1-4*x^2))/(2*x^2*(1-2*x-3*x^2+8*x^3-4*x^4)).
D-finite with recurrence -(n+2)*(87*n-587)*a(n) +2*(262*n^2-1391*n-1316)*a(n-1) +(-439*n^2+2325*n+3238)*a(n-2) +6*(-291*n^2+1878*n-3058)*a(n-3) +4*(787*n^2-5112*n+7910)*a(n-4) -8*(n-3)*(175*n-628)*a(n-5)=0. - R. J. Mathar, Mar 06 2022
PROG
(PARI) my(x='x+O('x^40)); Vec((1-3*x-4*x^2+12*x^3 - (1-3*x-4*x^2+8*x^3)*sqrt(1-4*x^2))/(2*x^2*(1-2*x-3*x^2+8*x^3-4*x^4)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Aug 12 2021
STATUS
approved