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A099920 a(n) = (n+1)*F(n), F(n) = Fibonacci numbers A000045. 19

%I

%S 0,2,3,8,15,30,56,104,189,340,605,1068,1872,3262,5655,9760,16779,

%T 28746,49096,83620,142065,240812,407353,687768,1159200,1950650,

%U 3277611,5499704,9216519,15426870,25793240,43080608,71884197,119835652

%N a(n) = (n+1)*F(n), F(n) = Fibonacci numbers A000045.

%C A Fibonacci-Lucas convolution.

%C The number of edges in the Lucas cube L_(n+1) [Klavzar]. - _R. J. Mathar_, Nov 05 2008

%C Sums of rows of the triangle in A108037. - _Reinhard Zumkeller_, Oct 07 2012

%D A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 35.

%H Reinhard Zumkeller, <a href="/A099920/b099920.txt">Table of n, a(n) for n = 0..1000</a>

%H S. Klavzar, <a href="http://dx.doi.org/10.1016/j.disc.2004.02.023">On median nature and enumerative properties of Fibonacci-like cubes</a>, Discr. Math. 299 (2005), 145-153.

%H Franck Ramaharo, <a href="https://arxiv.org/abs/1807.05256">A one-variable bracket polynomial for some Turk's head knots</a>, arXiv:1807.05256 [math.CO], 2018.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1)

%F G.f.: x*(2-x)/(1-x-x^2)^2;

%F a(n) = sum{k=0..n, F(n-k)*(L(k-1)+0^k)};

%F a(n) = sum{k=0..n+1, F(n-k)*binomial(n-k+1, k)*binomial(1, (k+1)/2)*(1-(-1)^k)/2}.

%F a(0)=0, a(1)=2, a(2)=3, a(3)=8, a(n) = 2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). - _Harvey P. Dale_, Jan 18 2012

%F a(n) = a(n-1) + a(n-2) + A000032(n-1) (Lucas numbers). - _Bob Selcoe_, Aug 19 2015

%t Table[Fibonacci[n](n+1),{n,0,40}] (* or *) LinearRecurrence[{2,1,-2,-1},{0,2,3,8},40] (* _Harvey P. Dale_, Jan 18 2012 *)

%o (MAGMA) [(n+1)*Fibonacci(n): n in [0..60]]; // _Vincenzo Librandi_, Apr 23 2011

%o (Haskell)

%o a099920 n = a099920_list !! n

%o a099920_list = zipWith (*) [1..] a000045_list

%o -- _Reinhard Zumkeller_, Oct 07 2012

%o (PARI) a(n)=(n+1)*fibonacci(n) \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Equals A010049(n) + A001629(n+1).

%Y Cf. A000045, A000032, A045925, A023607.

%K nonn,easy

%O 0,2

%A _Paul Barry_ and _Ralf Stephan_, Oct 15 2004

%E Entry revised by _N. J. A. Sloane_, Jan 23 2006. The offset changed, so some of the formulas may now be slightly off.

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Last modified September 15 04:09 EDT 2019. Contains 327062 sequences. (Running on oeis4.)