OFFSET
1,2
COMMENTS
This is half the number of edges of the origami flip graph of the all-equal-angle single-vertex crease pattern of degree 2n.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1658
Thomas C. Hull, Manuel Morales, Sarah Nash, and Natalya Ter-Saakov, Maximal origami flip graphs of flat-foldable vertices: properties and algorithms, arXiv:2203.14173 [math.CO], 2022.
FORMULA
G.f.: x*(2*x+1)/(1-4*x)^(3/2).
D-finite with recurrence (-n+1)*a(n) +2*(n+2)*a(n-1) +4*(2*n-5)*a(n-2)=0. - R. J. Mathar, Mar 29 2022
MAPLE
a:=n->(n+1)*(3*n-2)*binomial(2*n, n-1)/(4*n-2):
seq(a(n), n=1..33);
MATHEMATICA
a[n_] := (n + 1)*(3*n - 2)*Binomial[2*n, n - 1]/(4*n - 2); Array[a, 25] (* Amiram Eldar, Mar 25 2022 *)
PROG
(PARI) a(n) = (n+1)*(3*n-2)*binomial(2*n, n-1)/(4*n-2); \\ Michel Marcus, Mar 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Natalya Ter-Saakov, Mar 24 2022
STATUS
approved