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A081071
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Lucas(4n+2)-2, or Lucas(2n+1)^2.
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5
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1, 16, 121, 841, 5776, 39601, 271441, 1860496, 12752041, 87403801, 599074576, 4106118241, 28143753121, 192900153616, 1322157322201, 9062201101801, 62113250390416, 425730551631121, 2918000611027441, 20000273725560976
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OFFSET
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0,2
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COMMENTS
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Conjecture: a(n)= Fibonacci(4n+3) + sum_{k=2..2n} Fibonacci(2k). [From Alex Ratushnyak, May 06 2012]
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REFERENCES
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Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,-8,1).
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FORMULA
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a(n) = 8a(n-1)-8a(n-2)+a(n-3).
a(n ) =-2+(3/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/2)*sqrt(5)*{[(7/2)+(3/2) *sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0. [From Paolo P. Lava, Dec 01 2008]
G.f.: -(1+8*x+x^2)/((x-1)*(x^2-7*x+1)). [Colin Barker, Jun 26 2012]
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MAPLE
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luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 40 do printf(`%d, `, luc(4*n+2)-2) od:
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MATHEMATICA
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CoefficientList[Series[-(1+8*x+x^2)/((x-1)*(x^2-7*x+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -8, 1}, {1, 16, 121}, 50] (* Vincenzo Librandi, 26 jun 2012 *)
LucasL[4*Range[0, 20]+2]-2 (* Harvey P. Dale, Nov 25 2012 *)
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PROG
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(MAGMA) I:=[1, 16, 121]; [n le 3 select I[n] else 8*Self(n-1)-8*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 26 2012
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CROSSREFS
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Cf. A000032 (Lucas numbers), A002878 is Lucas(2n+1).
Sequence in context: A082921 A191902 A014765 * A217022 A069658 A069667
Adjacent sequences: A081068 A081069 A081070 * A081072 A081073 A081074
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KEYWORD
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nonn,easy
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AUTHOR
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R. K. Guy, Mar 04, 2003
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EXTENSIONS
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More terms and Maple code from James A. Sellers, Mar 05, 2003
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STATUS
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approved
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