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A140167
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a(n) = (-1)*a(n-1) + 3*a(n-2).
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4
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-1, 1, -4, 7, -19, 40, -97, 217, -508, 1159, -2683, 6160, -14209, 32689, -75316, 173383, -399331, 919480, -2117473, 4875913, -11228332, 25856071, -59541067, 137109280, -315732481, 727060321
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OFFSET
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1,3
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COMMENTS
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A140165 is a companion sequence.
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LINKS
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Table of n, a(n) for n=1..26.
Index to sequences with linear recurrences with constant coefficients, signature (-1,3). [From R. J. Mathar, Dec 12 2009]
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FORMULA
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a(n) = (-1)*a(n-1) + 3*a(n-2), given a(1) = -1, a(2) = 1. a(n) = term (1,2) of X^n, where X = the 2x2 matrix [1,-1; -1,-2].
a(n)=-(1/2)*[-1/2+(1/2)*sqrt(13)]^n-(1/2)*[-1/2-(1/2)*sqrt(13)]^n-(1/26)*sqrt(13)*[-1/2-(1/2) *sqrt(13)]^n+(1/26)*[-1/2+(1/2)*sqrt(13)]^n*sqrt(13), with n>=0 [From Paolo P. Lava, Aug 01 2008]
a(n)=(-1)^n*A006130(n-1). G.f.: -x/(1+x-3*x^2). [From R. J. Mathar, Dec 12 2009]
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EXAMPLE
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a(5) = -19 = (-1)*7 + 3*(-4).
a(5) = -19 = term (1,2) of X^5 since X^5 = [ -2, -19; -19, -59].
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CROSSREFS
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Cf. A140165.
Sequence in context: A006381 A102991 A062306 * A006130 A182228 A182646
Adjacent sequences: A140164 A140165 A140166 * A140168 A140169 A140170
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KEYWORD
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sign
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AUTHOR
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Gary W. Adamson, May 10 2008
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STATUS
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approved
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