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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A022087, A019274, A006355, A001610.

Programs

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

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 *)

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

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]

Extensions

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