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A256233
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a(n) = L(2*n+1) - 2, where L is A000032.
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2
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-1, 2, 9, 27, 74, 197, 519, 1362, 3569, 9347, 24474, 64077, 167759, 439202, 1149849, 3010347, 7881194, 20633237, 54018519, 141422322, 370248449, 969323027, 2537720634, 6643838877, 17393795999, 45537549122, 119218851369, 312119004987, 817138163594
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)).
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).
a(n) = (-2+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5))))/sqrt(5)). - Colin Barker, Nov 03 2016
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MATHEMATICA
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Table[LucasL[n] - 2, {n, 1, 70, 2}] (* or *) LinearRecurrence[{4, -4, 1}, {-1, 2, 9}, 40]
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PROG
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(Magma) [Lucas(n)-2: n in [1..70 by 2]];
(PARI) Vec((-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Nov 03 2016
(PARI) L(n) = round(((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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