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

0,1

Comments

Fibonacci sequence beginning 27, 2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..202

Index entries for linear recurrences with constant coefficients, signature (1,1).

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

Maple

a:= n-> (<<0|1>, <1|1>>^n. <<27, 2>>)[1, 1]:
seq(a(n), n=0..50);  # Alois P. Heinz, Nov 18 2018

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 *)

Prog

(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
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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
(Maxima) makelist(coeff(taylor((25*x-27)/(x^2+x-1), x, 0, n), x, n), n, 0, 33);  /* Bruno Berselli, Jun 20 2011 */
(PARI) a(n)=27*fibonacci(n-1)+2*fibonacci(n) \\ Charles R Greathouse IV, Jun 20 2011
(SageMath) [2*fibonacci(n+1) + 25*fibonacci(n-1) for n in range(101)] # G. C. Greubel, Oct 26 2022

Crossrefs

Cf. A000045, A000032, A157681.

Sequence in context: A040726 A040727 A059953 * A036195 A040728 A040716

Adjacent sequences: A190991 A190992 A190993 * A190995 A190996 A190997

Keyword

nonn,easy,less

Author

Vladimir Joseph Stephan Orlovsky, Jun 06 2011

Status

approved