OFFSET
0,4
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., Enumerations of peaks and valleys on non-decreasing Dyck paths, Discrete Mathematics (2018), 341(10), 2789-2807.
Index entries for linear recurrences with constant coefficients, signature (5,-7,2).
FORMULA
From Colin Barker, Apr 09 2019: (Start)
a(n) = 2^(-3-n)*(-3*4^n + 4*(3-sqrt(5))^n*(3+sqrt(5)) - 4*(-3+sqrt(5))*(3+sqrt(5))^n) for n>2.
a(n) = 5*a(n-1) - 7*a(n-2) + 2*a(n-3) n>5.
(End)
Note that Czabarka et al. give a g.f. for the whole triangle. - N. J. A. Sloane, Apr 09 2019
a(n) = A005248(n-1) -3*2^(n-3), n>=3. [Czabarka, Proposition 5 (2)] - R. J. Mathar, Apr 09 2019
MAPLE
(1-x)^2*x^2*(1+x)/(1-2*x)/(1-3*x+x^2) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 25 2018
PROG
(PARI) concat([0, 0], Vec(x^2*(1 - x)^2*(1 + x) / ((1 - 2*x)*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Apr 09 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 18 2018
STATUS
approved