A179023 a(n) = n(F(n+2) - 1) where F(n) is defined by A000045.

0, 1, 4, 12, 28, 60, 120, 231, 432, 792, 1430, 2552, 4512, 7917, 13804, 23940, 41328, 71060, 121752, 207955, 354200, 601776, 1020074, 1725552, 2913408, 4910425, 8263060, 13884156, 23297092, 39041772, 65349240, 109261887, 182492352

Offset

0,3

Comments

Let the 'Fibonacci weighted stars' T(i)'s be defined as: T(1) is an edge with one vertex as a distinguished vertex; the weight on the edge is taken to be F(1); for n>1, T(n) is formed by taking a copy of T(n-1) and attaching an edge to its distinguished vertex; the weight on the new edge is taken to be F(n). The sum of the weighted distances over all pairs of vertices in T(n) is this sequence.

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (4, -4, -2, 4, 0, -1).

Formula

a(0)=0, a(1)=1 and for n>1, a(n) = a(n-1) + F(n+1) +nF(n) -1.

a(n)= +4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6). = -n + A023607(n+1) - A000045(n+2). G.f.: -x*(-1+2*x^3) / ( (x-1)^2*(x^2+x-1)^2 ). - R. J. Mathar, Sep 15 2010

Mathematica

f[n_] := n(Fibonacci[n + 2] - 1); Array[f, 33, 0] (* Robert G. Wilson v, Jun 27 2010 *)

Crossrefs

Sequence in context: A182705 A186924 A261320 * A321690 A269712 A028399

Adjacent sequences: A179020 A179021 A179022 * A179024 A179025 A179026

Keyword

nonn,easy

Author

K.V.Iyer, Jun 25 2010

Extensions

More terms from Robert G. Wilson v, Jun 27 2010

Status

approved