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A081069
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Lucas(4n)+2, or Lucas(2n)^2.
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1
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4, 9, 49, 324, 2209, 15129, 103684, 710649, 4870849, 33385284, 228826129, 1568397609, 10749957124, 73681302249, 505019158609, 3461452808004, 23725150497409, 162614600673849, 1114577054219524, 7639424778862809
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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FORMULA
| a(n) = 8a(n-1)-8a(n-2)+a(n-3)
a(n)=2+[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Dec 01 2008]
a(n)=2^(4*n)*(cos(Pi/5)^(2*n)+cos(3*Pi/5)^(2*n))^2 [From Gary Detlefs (gdetlefs(At)aol.com), Dec 5 2010]
a(n) = 7*a(n-1)-a(n-2)-10, n>1 [From Gary Detlefs (gdetlefs(At)aol.com), Dec 6 2010]
a(n)=5*sum(fibonacci(4*k+2),k=0..n)+4, with ofset -1,[From Gary Detlefs (gdetlefs(At)aol.com), Dec 6 2010]
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MAPLE
| 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) od:
G:=(x, n)-> cos(x)^n +cos(3*x)^n: seq(simplify(2^(4*n)*G(Pi/5, 2*n)^2), n=0..19)[From Gary Detlefs (gdetlefs(At)aol.com), Dec 5 2010]
t:= n-> sum(fibonacci(4*k+2), k=0..n):seq(5*t(n)+4, n=-1..18); [From Gary Detlefs (gdetlefs(At)aol.com), Dec 6 2010]
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PROG
| (MAGMA) [ Lucas(2*n)^2: n in [0..70] ]; // Vincenzo Librandi, Apr 16 2011
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CROSSREFS
| Cf. A000032 (Lucas numbers).
Sequence in context: A068809 A110481 A030088 * A053967 A028945 A082875
Adjacent sequences: A081066 A081067 A081068 * A081070 A081071 A081072
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KEYWORD
| nonn,easy
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Mar 04, 2003
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 05, 2003
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