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A135030
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Generalized Fibonacci numbers: a(n) = 6*a(n-1) + 2*a(n-2).
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9
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0, 1, 6, 38, 240, 1516, 9576, 60488, 382080, 2413456, 15244896, 96296288, 608267520, 3842197696, 24269721216, 153302722688, 968355778560, 6116740116736, 38637152257536, 244056393778688, 1541612667187200
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OFFSET
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0,3
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COMMENTS
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For n>0, a(n) equals the number of words of length n-1 over {0,1,...,7} 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(0) = 0; a(1) = 1; a(n) = 2*(3*a(n-1) + a(n-2)).
a(n) = 1/(2*sqrt(11))*( (3 + sqrt(11))^n - (3 - sqrt(11))^n ).
E.g.f.: (1/sqrt(11))*exp(3*x)*sinh(sqrt(11)*x). - G. C. Greubel, Sep 17 2016
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MAPLE
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A:= gfun:-rectoproc({a(0) = 0, a(1) = 1, a(n) = 2*(3*a(n-1) + a(n-2))}, a(n), remember):
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MATHEMATICA
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LinearRecurrence[{6, 2}, {0, 1}, 30] (* or *) CoefficientList[Series[ -(x/(2x^2+6x-1)), {x, 0, 30}], x] (* Harvey P. Dale, Jun 20 2011 *)
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PROG
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(Sage) [lucas_number1(n, 6, -2) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 6*Self(n-1) + 2*Self(n-2): n in [1..35]]; // Vincenzo Librandi, Sep 18 2016
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CROSSREFS
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Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226, A180250.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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