This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179023 #17 Jul 30 2015 23:23:08 %S A179023 0,1,4,12,28,60,120,231,432,792,1430,2552,4512,7917,13804,23940,41328, %T A179023 71060,121752,207955,354200,601776,1020074,1725552,2913408,4910425, %U A179023 8263060,13884156,23297092,39041772,65349240,109261887,182492352 %N A179023 a(n) = n(F(n+2) - 1) where F(n) is defined by A000045. %C A179023 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. %H A179023 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, -2, 4, 0, -1). %F A179023 a(0)=0, a(1)=1 and for n>1, a(n) = a(n-1) + F(n+1) +nF(n) -1. %F A179023 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 %t A179023 f[n_] := n(Fibonacci[n + 2] - 1); Array[f, 33, 0] (* _Robert G. Wilson v_, Jun 27 2010 *) %K A179023 nonn,easy %O A179023 0,3 %A A179023 _K.V.Iyer_, Jun 25 2010 %E A179023 More terms from _Robert G. Wilson v_, Jun 27 2010