A374259 a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3), with a(0)=4, a(1)=6, a(2)=20.

4, 6, 20, 48, 130, 336, 884, 2310, 6052, 15840, 41474, 108576, 284260, 744198, 1948340, 5100816, 13354114, 34961520, 91530452, 239629830, 627359044, 1642447296, 4299982850, 11257501248, 29472520900, 77160061446, 202007663444, 528862928880, 1384581123202, 3624880440720, 9490060198964

Offset

0,1

Comments

a(n) is the number of edge covers of a rocket graph R_{3,n,n}.

A rocket graph R_{3,n,n} is cycle graph C_3 with two paths of n edges, where an end vertex of each path is identified with a distinct vertex in the C_3.

In other words, a rocket graph is a path with vertices -n-1, ..., -1, 0, 1, ..., n+1 with an additional edge (-1,1).

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

Formula

G.f.: (4-2*x)/(1-2*x-2*x^2+x^3).

a(n) = 2*A059929(n+1).

a(n) = Fibonacci(2n+2)+3*Fibonacci(n+1)*Fibonacci(n+1).

Example

For n=1, the R_{3,1,1} rocket graph is as follows and has a(1)=6 edge covers.
    *--*
   /|
  * |
   \|
    *--*

Mathematica

LinearRecurrence[{2, 2, -1}, {4, 6, 20}, 50] (* Paolo Xausa, Jul 20 2024 *)

Crossrefs

Equals twice A059929.

Sequence in context: A079435 A227959 A088015 * A375362 A027377 A048789

Adjacent sequences: A374256 A374257 A374258 * A374260 A374261 A374262

Keyword

nonn,easy

Author

Bridget Rozema, Jul 01 2024

Status

approved