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A072263
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a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=2, a(1)=3.
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8
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2, 3, 19, 72, 311, 1293, 5434, 22767, 95471, 400248, 1678099, 7035537, 29497106, 123669003, 518492539, 2173822632, 9113930591, 38210904933, 160202367754, 671661627927, 2815996722551, 11806298307288, 49498878534619, 207528127140297
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OFFSET
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0,1
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COMMENTS
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Inverse binomial transform of A087130. - Johannes W. Meijer, Aug 01 2010
Pisano period lengths: 1, 3, 4, 6, 4, 12, 3, 12, 12, 12, 120, 12, 12, 3, 4, 24, 288, 12, 72, 12... - R. J. Mathar, Aug 10 2012
This is the Lucas sequence V(3,-5). - Bruno Berselli, Jan 09 2013
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LINKS
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Table of n, a(n) for n=0..23.
Wikipedia, Lucas sequence: Specific names.
Index to sequences with linear recurrences with constant coefficients, signature (3,5).
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FORMULA
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a(n) = 2*A015523(n+1)-3*A015523(n).
a(n) = ((3+sqrt(29))/2)^n + ((3-sqrt(29))/2)^n.
G.f.: (2-3*x)/(1-3*x-5*x^2). - R. J. Mathar, Feb 06 2010
Contribution from Johannes W. Meijer, Aug 01 2010: (Start)
Limit(a(n+k)/a(k), k=infinity) = (A072263(n)+A015523(n)*sqrt(29))/2
Limit(A072263(n)/A015523(n)) = sqrt(29). (End)
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EXAMPLE
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a(5)=5*b(4)+b(6): 1293=5*57+1008.
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PROG
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(Sage) [lucas_number2(n, 3, -5) for n in xrange(0, 16)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
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Cf. A072264, A152187, A197189.
Appears in A179606 and A015523. - Johannes W. Meijer, Aug 01 2010
Sequence in context: A128968 A153409 A143893 * A009178 A141508 A119344
Adjacent sequences: A072260 A072261 A072262 * A072264 A072265 A072266
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KEYWORD
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nonn,easy
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AUTHOR
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Miklos Kristof, Jul 08 2002
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EXTENSIONS
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Offset changed and terms added by Johannes W. Meijer, Jul 19 2010
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STATUS
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approved
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