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A087124 a(n) = Fibonacci(n) + Fibonacci(2n+1). 3

%I #22 Sep 08 2022 08:45:11

%S 1,3,6,15,37,94,241,623,1618,4215,11001,28746,75169,196651,514606,

%T 1346879,3525565,9229062,24160401,63250167,165586906,433505383,

%U 1134920881,2971243730,7778788417,20365086099,53316412566,139584058863

%N a(n) = Fibonacci(n) + Fibonacci(2n+1).

%C Binomial transform of A087123.

%C For n>=1, a(n) is the coefficient of x in the reduction by x^2->x+1 of the polynomial 1+x^n+x^(2n+1). For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232. - _Clark Kimberling_, Jul 01 2011

%H Vincenzo Librandi, <a href="/A087124/b087124.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-2,1).

%F G.f.: (1-2*x)*(1+x-x^2)/((1-3*x+x^2)*(1-x-x^2)). - _Colin Barker_, Mar 12 2012

%t CoefficientList[Series[(1-2*x)*(1+x-x^2)/((1-3*x+x^2)*(1-x-x^2)),{x,0,1001}],x] (* _Vincenzo Librandi_, Mar 13 2012 *)

%o (Magma) [Fibonacci(n)+Fibonacci(2*n+1): n in [0..40]]; // _Vincenzo Librandi_, Mar 13 2012

%o (PARI) a(n)=fibonacci(n)+fibonacci(2*n+1) \\ _Charles R Greathouse IV_, Mar 13 2012

%Y Cf. A000045.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Aug 15 2003

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)