OFFSET
1,3
LINKS
E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.
Index entries for linear recurrences with constant coefficients, signature (6,-9,-5,15,-1,-4,1)
FORMULA
G.f.: z^2*(1-z-2z^2+3z^3-2z^4)/[(1+z)(1-3z+z^2)^2*(1-z-z^2)].
a(n) ~ (5-sqrt(5)) * (3+sqrt(5))^n * n / (5 * 2^(n+2)). - Vaclav Kotesovec, Mar 20 2014
EXAMPLE
a(3)=5 because we have UDUDUD, UDU(U)DD, U(U)DDUD, U(U)D(U)DD and U(U)UDDD, the up steps starting at an odd level being shown between parentheses (U=(1,1), D=(1,-1)).
MAPLE
G:=z^2*(1-z-2*z^2+3*z^3-2*z^4)/(1+z)/(1-3*z+z^2)^2/(1-z-z^2): Gser:=series(G, z=0, 34): seq(coeff(Gser, z, n), n=1..30);
MATHEMATICA
Rest[CoefficientList[Series[x^2*(1-x-2*x^2+3*x^3-2*x^4)/(1+x)/(1-3*x+x^2)^2/(1-x-x^2), {x, 0, 20}], x]] (* Vaclav Kotesovec, Mar 20 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 05 2006
STATUS
approved