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A179023
a(n) = n(F(n+2) - 1) where F(n) is defined by A000045.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
K.V.Iyer, Jun 25 2010
EXTENSIONS
More terms from Robert G. Wilson v, Jun 27 2010
STATUS
approved