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
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
KEYWORD
nonn,easy
AUTHOR
K.V.Iyer, Jun 25 2010
EXTENSIONS
More terms from Robert G. Wilson v, Jun 27 2010
STATUS
approved