OFFSET
0,5
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
E. Czabarka et al, Enumerations of peaks and valleys on non-decreasing Dyck paths, Disc. Math. 341 (2018) 2789-2807.
Index entries for linear recurrences with constant coefficients, signature (7,-17,16,-4).
FORMULA
a(n) = 7*a(n-1) - 17*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>7. - Colin Barker, Apr 11 2019
MAPLE
(1-x)^2*x^3*(1+x-3*x^2)/(1-2*x)^2/(1-3*x+x^2) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 25 2018
MATHEMATICA
LinearRecurrence[{7, -17, 16, -4}, {0, 0, 0, 1, 6, 21, 68, 208}, 50] (* Paolo Xausa, May 24 2024 *)
PROG
(PARI) concat([0, 0, 0], Vec(x^3*(1 - x)^2*(1 + x - 3*x^2) / ((1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Apr 11 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 18 2018
STATUS
approved