OFFSET
0,3
COMMENTS
Equivalently, the number of closed convex paths of length n whose steps are the 10th roots of unity up to translation. For even n, there will be 5 paths of zero area consisting of n/2 steps in one direction followed by n/2 steps in the opposite direction.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,7,3,-8,3,7,-6,-4,4,1,-1)
FORMULA
G.f.: (1 - x^10)/((1 - x^2)^5 * (1 - x^5)^2).
G.f.: (1 - x + x^2 - x^3 + x^4)/((1 + x + x^2 + x^3 + x^4)*(1 - x)^6*(1 + x)^4).
MATHEMATICA
LinearRecurrence[{1, 4, -4, -6, 7, 3, -8, 3, 7, -6, -4, 4, 1, -1}, {1, 0, 5, 0, 15, 2, 35, 10, 70, 30, 128, 70, 220, 140}, 50] (* Jinyuan Wang, Feb 28 2020 *)
PROG
(PARI) Vec((1 - x^10)/((1 - x^2)^5 * (1 - x^5)^2) + O(x^50))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Nov 09 2018
STATUS
approved