A352626 a(n) = (n+1)*(3*n-2)*C(2*n,n-1)/(4*n-2).

1, 8, 42, 200, 910, 4032, 17556, 75504, 321750, 1361360, 5727436, 23984688, 100053772, 416024000, 1725013800, 7135405920, 29452939110, 121347523440, 499132441500, 2050025300400, 8408638258020, 34448503964160, 140974630569240, 576340150932000, 2354075068866300

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

a(n) = A002457(n-1)+2*A002457(n-2). - 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

Number of vertices of the origami flip graph of the all-equal-angle single-vertex crease pattern of degree 2n is A162551.

Sequence in context: A093381 A097788 A171478 * A276265 A249977 A037710

Adjacent sequences: A352623 A352624 A352625 * A352627 A352628 A352629

Keyword

nonn,easy

Author

Natalya Ter-Saakov, Mar 24 2022

Status

approved