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A015555
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Expansion of x/(1 - 7*x - 2*x^2).
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6
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0, 1, 7, 51, 371, 2699, 19635, 142843, 1039171, 7559883, 54997523, 400102427, 2910712035, 21175189099, 154047747763, 1120684612539, 8152887783299, 59311583708171, 431486861523795, 3139031198082907, 22836192109627939
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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,...,8} 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) = 7*a(n-1) + 2*a(n-2).
E.g.f.: (exp(x*(7 + sqrt(57))/2) - exp(x*(7 - sqrt(57))/2))/sqrt(57). - Iain Fox, Dec 30 2017
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MATHEMATICA
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PROG
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(Sage) [lucas_number1(n, 7, -2) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 7*Self(n-1) + 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-2*x^2))) \\ G. C. Greubel, Dec 30 2017
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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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