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 A168674 a(n) = 2*A001610(n). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 2 10:43 EST 2024. Contains 370466 sequences. (Running on oeis4.)