A167375 a(n)=3*a(n-1)-a(n-2) with a(0)=1, a(1)=3, a(2)=11.

1, 3, 11, 30, 79, 207, 542, 1419, 3715, 9726, 25463, 66663, 174526, 456915, 1196219, 3131742, 8199007, 21465279, 56196830, 147125211, 385178803, 1008411198, 2640054791, 6911753175, 18095204734, 47373861027, 124026378347, 324705274014, 850089443695

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3, -1).

Formula

a(n) = (-1)^n*A098150(n-1), n>0.

G.f.: (3*x^2+1)/(1-3*x+x^2).

a(n) = 3*L(2n+1)-F(2n), where F(n) is the n-th Fibonacci number and L(n) is the n-th Lucas number. - Rigoberto Florez, Dec 24 2018

Mathematica

Join[{1}, LinearRecurrence[{3, -1}, {3, 11}, 30]] (* Harvey P. Dale, Jun 25 2014 *)
CoefficientList[Series[(3 x^2 + 1)/(1 - 3 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2014 *)
Table[3LucasL[2n+1]-Fibonacci[2n], {n, 0, 20}] (* Rigoberto Florez, Dec 24 2018 *)

Prog

(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 3*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jun 26 2014

Crossrefs

Cf. A135929, A138034.

Sequence in context: A165893 A106397 A295144 * A098150 A346848 A372480

Adjacent sequences: A167372 A167373 A167374 * A167376 A167377 A167378

Keyword

nonn,easy

Author

Jamel Ghanouchi, Nov 02 2009

Extensions

Edited by R. J. Mathar, Nov 03 2009

Status

approved