A190994 a(n) = a(n-1) + a(n-2), for n>=2, with a(0)=27, a(1)=2.
27, 2, 29, 31, 60, 91, 151, 242, 393, 635, 1028, 1663, 2691, 4354, 7045, 11399, 18444, 29843, 48287, 78130, 126417, 204547, 330964, 535511, 866475, 1401986, 2268461, 3670447, 5938908, 9609355, 15548263, 25157618, 40705881, 65863499
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..202
- Index entries for linear recurrences with constant coefficients, signature (1,1).
Programs
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Magma
[n eq 1 select 27 else n eq 2 select 2 else Self(n-1)+Self(n-2): n in [1..40]]; // Klaus Brockhaus, Jun 20 2011
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Magma
Z
:=PolynomialRing(Integers()); N :=NumberField(x^2-5); S:=[ 27/2*((1/2+1/2*r)^n+(1/2-1/2*r)^n)+23/10*r*((1/2-1/2*r)^n-(1/2+1/2*r)^n): n in [0..39] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jun 20 2011 -
Maple
a:= n-> (<<0|1>, <1|1>>^n. <<27, 2>>)[1,1]: seq(a(n), n=0..50); # Alois P. Heinz, Nov 18 2018
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Mathematica
LinearRecurrence[{1, 1}, {27, 2}, 100] CoefficientList[Series[(25x-27)/(x^2+x-1),{x,0,100}],x] (* Harvey P. Dale, Jun 19 2011 *) -
Maxima
makelist(coeff(taylor((25*x-27)/(x^2+x-1), x, 0, n), x, n), n, 0, 33); /* Bruno Berselli, Jun 20 2011 */
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PARI
a(n)=27*fibonacci(n-1)+2*fibonacci(n) \\ Charles R Greathouse IV, Jun 20 2011
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SageMath
[2*fibonacci(n+1) + 25*fibonacci(n-1) for n in range(101)] # G. C. Greubel, Oct 26 2022
Formula
G.f.: (27-25*x)/(1-x-x^2). - Harvey P. Dale, Jun 19 2011
a(n) = (27/2)*( ((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n ) + (23/10)*sqrt(5)*( ((1-sqrt(5))/2)^n - ((1+sqrt(5))/2)^n ). - Antonio Alberto Olivares, Jun 19 2011, corrected by Klaus Brockhaus, Jun 20 2011
a(n) = 2*Fibonacci(n) + 27*Fibonacci(n-1). - Charles R Greathouse IV, Jun 20 2011
a(n) = 2*LucasL(n) + 25*Fibonacci(n-1). - G. C. Greubel, Oct 26 2022
Comments