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A015579 Expansion of x/(1-9x-2x^2). 9
0, 1, 9, 83, 765, 7051, 64989, 599003, 5521005, 50887051, 469025469, 4323003323, 39845080845, 367251734251, 3384955769949, 31199105398043, 287561860122285, 2650454951896651, 24429218287314429, 225163874489623163, 2075333306981237325, 19128327511810382251 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,2).

FORMULA

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

a(n) = (1/89)*sqrt(89)*{[(9/2) + (1/2)*sqrt(89)]^n - [(9/2) - (1/2)*sqrt(89)]^n}, with n>=0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b+2*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

LinearRecurrence[{9, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 9, -2) for n in xrange(0, 19)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n le 2 select n-1 else 9*Self(n-1) + 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

CROSSREFS

Cf. A099371.

Sequence in context: A048353 A037502 A037679 * A162759 A147960 A155499

Adjacent sequences:  A015576 A015577 A015578 * A015580 A015581 A015582

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Extended by T. D. Noe, May 23 2011

STATUS

approved

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Last modified October 20 05:42 EDT 2017. Contains 293601 sequences.