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A015580
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Expansion of x/(1-9x-4x^2).
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1
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0, 1, 9, 85, 801, 7549, 71145, 670501, 6319089, 59553805, 561260601, 5289560629, 49851088065, 469818035101, 4427766668169, 41729172153925, 393273616058001, 3706379233137709, 34930507562471385, 329200084994793301, 3102522795203025249, 29239505496806400445
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (9,4)
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FORMULA
| a(n) = 9 a(n-1) + 4 a(n-2).
a(n)=(1/97)*sqrt(97)*{[(9/2)+(1/2)*sqrt(97)]^n-[(9/2)-(1/2)*sqrt(97)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 13 2009]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=9*b+4*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 9, -4) for n in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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CROSSREFS
| Cf. A015579, A099371.
Sequence in context: A166902 A196434 A197197 * A163308 A160112 A108427
Adjacent sequences: A015577 A015578 A015579 * A015581 A015582 A015583
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Extended by T. D. Noe (noe(AT)sspectra.com), May 23 2011
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