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Search: id:A075155
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| A075155 |
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Cubes of Lucas numbers. |
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+0
4
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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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)=3(-1)^n*L(n)+L(3n). Also a(n)=(-1)^n*A075151(n)
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FORMULA
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a(n)=L(n)*C(n)^2, L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084).
a(n)=3a(n-1)+6a(n-2)-3a(n-3)-a(n-4), a(0)=8, a(1)=1, a(2)=27, a(3)=64. G.f.: (8-23*x-24*x^2+x^3)/(1-3*x-6*x^2+3*x^3+x^4).
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MAPLE
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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
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Cf. A000032, A061084, A075150, A075151.
Third row of array A103324.
Sequence in context: A002173 A050458 A125166 this_sequence A075151 A028943 A050311
Adjacent sequences: A075152 A075153 A075154 this_sequence A075156 A075157 A075158
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Sep 06 2002
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EXTENSIONS
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Simpler definition from Ralf Stephan, Nov 01 2004
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