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A127357
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Expansion of 1/(1-2*x+9*x^2).
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2
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1, 2, -5, -28, -11, 230, 559, -952, -6935, -5302, 51811, 151340, -163619, -1689298, -1906025, 11391632, 39937489, -22649710, -404736821, -605626252, 2431378885, 10313394038, -1255621889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform of A100193. A member of the family of sequences with g.f. 1/(1-2*x+r^2*x^2) which are the Hankel transforms of the sequences given by sum{k=0..n, C(2*n,k)*r^(n-k)}.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,-9)
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FORMULA
| a(n) = sum{k=0..n, C(n-k,k)*2^(n-2*k)*(-9)^k}.
a(n) = 2*a(n-1) -9*a(n-2), n>=2. - Vincenzo Librandi, Mar 22 2011
a(n) = ((1-2*sqrt(2)*i)^n-(1+2*sqrt(2)*i)^n)*i/(4*sqrt(2)), where i=sqrt(-1) - Bruno Berselli, Jul 01 2011
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MATHEMATICA
| Join[{a=1, b=2}, Table[c=2*b-9*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (Sage) [lucas_number1(n, 2, 9) for n in xrange(1, 24)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(MAGMA) m:=23; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-2*x+9*x^2))); // Bruno Berselli, Jul 01 2011
(Maxima) makelist(coeff(taylor(1/(1-2*x+9*x^2), x, 0, n), x, n), n, 0, 22); [Bruno Berselli, Jul 01 2011]
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CROSSREFS
| Sequence in context: A058182 A057438 A002795 * A025170 A151775 A095159
Adjacent sequences: A127354 A127355 A127356 * A127358 A127359 A127360
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KEYWORD
| sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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