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 A015535 Expansion of x/(1 - 5*x - 2*x^2). 14
 0, 1, 5, 27, 145, 779, 4185, 22483, 120785, 648891, 3486025, 18727907, 100611585, 540513739, 2903791865, 15599986803, 83807517745, 450237562331, 2418802847145, 12994489360387, 69810052496225, 375039241201899, 2014816311001945, 10824160037413523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Pisano period lengths:  1, 1, 3, 2, 8, 3, 48, 2, 3, 8, 110, 6, 168, 48, 24, 4, 8, 3, 45, 8, ... - R. J. Mathar, Aug 10 2012 This is the Lucas sequence U(5,-2). - Bruno Berselli, Jan 08 2013 For n > 0, a(n) equals the number of  words of length n-1 over {0,1,...,6} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Wikipedia, Lucas sequence: Specific names. Index entries for linear recurrences with constant coefficients, signature (5,2). FORMULA a(n) = 5*a(n-1) + 2*a(n-2) with n > 1, a(0)=0, a(1)=1. a(n) = (1/33)*sqrt(33)*((5/2 + (1/2)*sqrt(33))^n - (5/2 - (1/2)*sqrt(33))^n). - Paolo P. Lava, Jan 13 2009 MATHEMATICA Join[{a=0, b=1}, Table[c=5*b+2*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *) LinearRecurrence[{5, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *) PROG (Sage) [lucas_number1(n, 5, -2) for n in range(0, 22)] # Zerinvary Lajos, Apr 24 2009 (MAGMA) [n le 2 select n-1 else 5*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-2*x^2))) \\ G. C. Greubel, Jan 01 2018 CROSSREFS Cf. A201002 (prime subsequence). Sequence in context: A257061 A052225 A293295 * A026292 A100193 A158869 Adjacent sequences:  A015532 A015533 A015534 * A015536 A015537 A015538 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)