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A081078
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Lucas(4n)-3, or Lucas(2n-1)*Lucas(2n+1).
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0
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4, 44, 319, 2204, 15124, 103679, 710644, 4870844, 33385279, 228826124, 1568397604, 10749957119, 73681302244, 505019158604, 3461452807999, 23725150497404, 162614600673844, 1114577054219519, 7639424778862804
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (8,-8,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2010]
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FORMULA
| a(n) = 8a(n-1)-8a(n-2)+a(n-3)
a(n)=-3+(7/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(3/2)*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]
G.f.: x*(-4-12*x+x^2) / ( (x-1)*(x^2-7*x+1)). a(n) = A056854(n)-3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 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 1 to 40 do printf(`%d, `, luc(4*n)-3) od:
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CROSSREFS
| Cf. A000032 (Lucas numbers).
Sequence in context: A074751 A129551 A202162 * A035014 A030987 A178294
Adjacent sequences: A081075 A081076 A081077 * A081079 A081080 A081081
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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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