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A015579
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Expansion of x/(1-9*x-2*x^2).
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10
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0, 1, 9, 83, 765, 7051, 64989, 599003, 5521005, 50887051, 469025469, 4323003323, 39845080845, 367251734251, 3384955769949, 31199105398043, 287561860122285, 2650454951896651, 24429218287314429, 225163874489623163, 2075333306981237325, 19128327511810382251
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,2).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(Sage) [lucas_number1(n, 9, -2) for n in range(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
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-2*x^2))) \\ G. C. Greubel, Jan 06 2018
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CROSSREFS
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Cf. A099371.
Sequence in context: A048353 A037502 A037679 * A162759 A147960 A155499
Adjacent sequences: A015576 A015577 A015578 * A015580 A015581 A015582
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Olivier Gérard
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EXTENSIONS
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Extended by T. D. Noe, May 23 2011
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STATUS
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approved
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