A168674 a(n) = 2*A001610(n).

0, 4, 6, 12, 20, 34, 56, 92, 150, 244, 396, 642, 1040, 1684, 2726, 4412, 7140, 11554, 18696, 30252, 48950, 79204, 128156, 207362, 335520, 542884, 878406, 1421292, 2299700, 3720994, 6020696, 9741692, 15762390, 25504084, 41266476, 66770562, 108037040

Offset

0,2

Comments

This sequence has a golden mean ratio limit.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 0, -1).

Formula

a(n) = 2*a(n-1) - a(n-3). [Dec 03 2009]

G.f.: 2*x*(2 - x)/((1-x)*(1 -x -x^2)). [Dec 03 2009]

Mathematica

M = {{0, 1}, {1, 1}} v[0] = {0, 1}; v[n_] := v[n] = M.v[n - 1] + {3, 2} a = Table[v[n][[1]], {n, 0, 30}]
LinearRecurrence[{2, 0, -1}, {0, 4, 6}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2012 *)
RecurrenceTable[{a[0] == 0, a[1] == 4, a[2] == 6, a[n] == 2 a[n-1] - a[n-3]}, a, {n, 50}] (* Vincenzo Librandi, Jul 30 2016 *)

Prog

(Magma) I:=[0, 4, 6]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 30 2016
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 0, 2]^n*[0; 4; 6])[1, 1] \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Cf. A022087, A019274, A006355, A001610.

Sequence in context: A019445 A119638 A178547 * A110935 A128034 A027150

Adjacent sequences: A168671 A168672 A168673 * A168675 A168676 A168677

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Jun 01 2010

Extensions

Definition simplified and notation in formulas set to OEIS standards by the Assoc. Editors of the OEIS, Dec 03 2009

Status

approved