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A015555 Expansion of x/(1 - 7*x - 2*x^2). 5
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).

a(n) = -(1/57)*sqrt(57)*(7/2 - (1/2)*sqrt(57))^n + (1/57)*sqrt(57)*(7/2 + (1/2)*sqrt(57))^n, with n>=0. - Paolo P. Lava, Jun 25 2008

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 xrange(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 September 23 23:21 EDT 2018. Contains 315306 sequences. (Running on oeis4.)