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 A015555 Expansion of x/(1 - 7*x - 2*x^2). 6
 0, 1, 7, 51, 371, 2699, 19635, 142843, 1039171, 7559883, 54997523, 400102427, 2910712035, 21175189099, 154047747763, 1120684612539, 8152887783299, 59311583708171, 431486861523795, 3139031198082907, 22836192109627939 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7,2). FORMULA 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 MATHEMATICA Join[{a=0, b=1}, Table[c=7*b+2*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *) LinearRecurrence[{7, 2}, {0, 1}, 30] (* Vincenzo Librandi Nov 13 2012 *) PROG (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 CROSSREFS Sequence in context: A037500 A037677 A034354 * A137382 A162757 A285880 Adjacent sequences: A015552 A015553 A015554 * A015556 A015557 A015558 KEYWORD nonn,easy AUTHOR Olivier Gérard STATUS approved

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Last modified August 13 17:42 EDT 2024. Contains 375144 sequences. (Running on oeis4.)