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A081068
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(Lucas(4n+2)+2)/5, or Fibonacci(2n+1)^2, or A081067/5.
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2
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1, 4, 25, 169, 1156, 7921, 54289, 372100, 2550409, 17480761, 119814916, 821223649, 5628750625, 38580030724, 264431464441, 1812440220361, 12422650078084, 85146110326225, 583600122205489, 4000054745112196, 27416783093579881
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 19.
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FORMULA
| a(n) = 8a(n-1)-8a(n-2)+a(n-3)
a(n)=(2/5)+(3/10)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/10)*sqrt(5)*{[(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]
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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)+2)/5) od:
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CROSSREFS
| Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A081067.
Equals A001519(n)^2 and A058038 - 1.
First differences of A103433.
Sequence in context: A128419 A006880 A175255 * A163072 A140177 A034494
Adjacent sequences: A081065 A081066 A081067 * A081069 A081070 A081071
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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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