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A015591 Expansion of x/(1 - 10x - 9x^2). 3
0, 1, 10, 109, 1180, 12781, 138430, 1499329, 16239160, 175885561, 1905008050, 20633050549, 223475577940, 2420453234341, 26215812544870, 283942204557769, 3075364358481520, 33309123425835121, 360769513484684890, 3907477245679364989, 42321698078155813900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths:  1, 2, 1, 4, 4, 2, 48, 8, 1, 4, 10, 4, 84, 48, 4, 16, 272, 2, 360, 4, ... - R. J. Mathar, Aug 10 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (10,9).

FORMULA

a(n) = 10*a(n-1) + 9*a(n-2).

a(n) = (1/68)*sqrt(34)*((5 + sqrt(34))^n - (5 - sqrt(34))^n), with n >= 0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=10*b+9*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Mar 29 2011 *)

LinearRecurrence[{10, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

PROG

(Sage) [lucas_number1(n, 10, -9) for n in range(0, 18)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n le 2 select n-1 else 10*Self(n-1) + 9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

CROSSREFS

Sequence in context: A198700 A320094 A267280 * A078922 A199760 A082181

Adjacent sequences:  A015588 A015589 A015590 * A015592 A015593 A015594

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Extended by T. D. Noe, May 23 2011

STATUS

approved

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Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)