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A015535
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Expansion of x/(1 - 5*x - 2*x^2).
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17
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0, 1, 5, 27, 145, 779, 4185, 22483, 120785, 648891, 3486025, 18727907, 100611585, 540513739, 2903791865, 15599986803, 83807517745, 450237562331, 2418802847145, 12994489360387, 69810052496225, 375039241201899, 2014816311001945, 10824160037413523
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OFFSET
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0,3
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COMMENTS
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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
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
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + 2*a(n-2) with n > 1, a(0)=0, a(1)=1.
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MATHEMATICA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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