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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 17 14:31 EDT 2019. Contains 328114 sequences. (Running on oeis4.)