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A081014
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a(n) = Lucas(4*n+1) + 1, or Lucas(2*n)*Lucas(2*n+1).
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1
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2, 12, 77, 522, 3572, 24477, 167762, 1149852, 7881197, 54018522, 370248452, 2537720637, 17393796002, 119218851372, 817138163597, 5600748293802, 38388099893012, 263115950957277, 1803423556807922, 12360848946698172
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OFFSET
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0,1
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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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FORMULA
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a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
G.f.: (2 -4*x -3*x^2)/((1-x)*(1-7*x+x^2)).
a(n) = 7*a(n-1) - a(n-2) - 5, n >= 2. - R. J. Mathar, Nov 07 2015
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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 25 do printf(`%d, `, luc(4*n+1)+1) od: # James A. Sellers, Mar 03 2003
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MATHEMATICA
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LinearRecurrence[{8, -8, 1}, {2, 12, 77}, 20] (* G. C. Greubel, Dec 24 2017 *)
CoefficientList[Series[(2-4x-3x^2)/((1-x)(1-7x+x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Aug 27 2021 *)
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PROG
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(PARI) vector(20, n, n--; f=fibonacci; f(4*n+2)+f(4*n)+1) \\ G. C. Greubel, Dec 24 2017
(Magma) I:=[2, 12, 77]; [n le 3 select I[n] else 8*Self(n-1) - 8*Self(n-2) + Self(n-3): n in [0..30]]; // G. C. Greubel, Dec 24 2017
(Sage) [lucas_number2(4*n+1, 1, -1) +1 for n in (0..20)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..20], n-> Lucas(1, -1, 4*n+1)[2] +1); # G. C. Greubel, Jul 14 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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