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A075151
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a(n)=L(n)^2*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084).
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1
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8, -1, 27, -64, 343, -1331, 5832, -24389, 103823, -438976, 1860867, -7880599, 33386248, -141420761, 599077107, -2537716544, 10749963743, -45537538411, 192900170952, -817138135549, 3461452853383, -14662949322176, 62113250509227, -263115950765039, 1114577054530568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n)=3*L(n)+(-1)^n*L(3n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-3,6,3,-1).
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FORMULA
| a(n)=-3a(n-1)+6a(n-2)+3a(n-3)-a(n-4), n>3.
G.f.: ( 8+23*x-24*x^2-x^3 ) / ( (x^2+x-1)*(x^2-4*x-1) ).
a(n) is asymptotic to (-phi)^(3n) where phi is the golden ratio (1+sqrt(5))/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 07 2002
a(n)=[ -2+sqrt(5)]^n+3*[1/2+(1/2)*sqrt(5)]^n+[ -2-sqrt(5)]^n+3*[1/2-(1/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 12 2008
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MATHEMATICA
| CoefficientList[Series[(8+23*x-24*x^2-x^3)/(1+3*x-6*x^2-3*x^3+x^4), {x, 0, 25}], x]
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CROSSREFS
| Cf. A000032, A061084, A001254, A075155.
Sequence in context: A050458 A125166 A075155 * A028943 A050311 A050302
Adjacent sequences: A075148 A075149 A075150 * A075152 A075153 A075154
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KEYWORD
| easy,sign
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002
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