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2, 5, 12, 30, 77, 200, 522, 1365, 3572, 9350, 24477, 64080, 167762, 439205, 1149852, 3010350, 7881197, 20633240, 54018522, 141422325, 370248452, 969323030, 2537720637, 6643838880, 17393796002, 45537549125, 119218851372, 312119004990, 817138163597, 2139295485800
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OFFSET
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0,1
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COMMENTS
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Luo proves that these integers cannot be uniquely decomposed as the sum of distinct and nonconsecutive terms of the Lucas number sequence. - Michel Marcus, Apr 20 2020
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LINKS
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FORMULA
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G.f.: ( -2+3*x ) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Mar 30 2011
a(n) = 2^(-1-n)*(2^(1+n)-(3-sqrt(5))^n*(-1+sqrt(5))+(1+sqrt(5))*(3+sqrt(5))^n). - Colin Barker, Nov 02 2016
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MAPLE
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f:= gfun:-rectoproc({a(n+3)-4*a(n+2)+4*a(n+1)-a(n), a(0) = 2, a(1) = 5, a(2) = 12}, a(n), remember):
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MATHEMATICA
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LinearRecurrence[{4, -4, 1}, {2, 5, 12}, 30] (* Harvey P. Dale, Oct 05 2015 *)
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PROG
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(PARI) a(n) = 5*fibonacci(n)*fibonacci(n+1) + 1 + (-1)^n; \\ Michel Marcus, Aug 26 2013
(PARI) Vec((-2+3*x)/((x-1)*(x^2-3*x+1)) + O(x^100)) \\ Altug Alkan, Jan 24 2016
(Magma) [5*Fibonacci(n)*Fibonacci(n+1)+1+(-1)^n: n in [0..40]]; // Vincenzo Librandi, Jan 24 2016
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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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