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A081070
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Lucas(4n)-2, or 5*Fibonacci(2n)^2.
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1
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0, 5, 45, 320, 2205, 15125, 103680, 710645, 4870845, 33385280, 228826125, 1568397605, 10749957120, 73681302245, 505019158605, 3461452808000, 23725150497405, 162614600673845, 1114577054219520, 7639424778862805
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, Arxiv preprint arXiv:1111.5626, 2011 (see Eq. 4).
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]
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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:
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PROG
| (MAGMA) [Lucas(4*n)-2: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
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CROSSREFS
| Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Equals 5*A049684.
Sequence in context: A027801 A079139 A188349 * A043025 A190540 A125836
Adjacent sequences: A081067 A081068 A081069 * A081071 A081072 A081073
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KEYWORD
| nonn,easy,changed
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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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