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A146078
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Expansion of 1/(1-x(1-9x)).
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5
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1, 1, -8, -17, 55, 208, -287, -2159, 424, 19855, 16039, -162656, -307007, 1156897, 3919960, -6492113, -41771753, 16657264, 392603041, 242687665, -3290739704, -5474928689, 24141728647, 73416086848, -143859470975, -804604252607
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OFFSET
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0,3
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COMMENTS
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Row sums of Riordan array (1,x(1-9x)).
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LINKS
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Table of n, a(n) for n=0..25.
Index to sequences with linear recurrences with constant coefficients, signature (1,-9).
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FORMULA
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a(n)=a(n-1)-9*a(n-2) ; a(0)=1, a(1)=1. a(n)=Sum_{k, 0<=k<=n}A109466(n,k)*9^(n-k).
a(n)=-(1/70)*I*sqrt(35)*[(1/2)+(1/2)*I*sqrt(35)]^n+(1/70)*I*sqrt(35)*[(1/2)-(1/2)*I *sqrt(35)]^n+(1/2)*[(1/2)+(1/2)*I*sqrt(35)]^n+(1/2)*[(1/2)-(1/2)*I*sqrt(35)]^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava, Nov 18 2008]
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MATHEMATICA
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Join[{a=1, b=1}, Table[c=b-9*a; a=b; b=c, {n, 80}]]
(*From Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)
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PROG
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(Sage) [lucas_number1(n, 1, 9) for n in xrange(1, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A010892, A107920, A106852, A106853, A106854, A145934, A145976, A145978.
Sequence in context: A111325 A173056 A008782 * A097058 A186255 A187987
Adjacent sequences: A146075 A146076 A146077 * A146079 A146080 A146081
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KEYWORD
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sign,easy
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AUTHOR
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Philippe DELEHAM, Oct 27 2008
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STATUS
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approved
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