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A324129
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a(n) = n*Fibonacci(n) + ((-1)^n + 1)/2.
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2
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1, 1, 3, 6, 13, 25, 49, 91, 169, 306, 551, 979, 1729, 3029, 5279, 9150, 15793, 27149, 46513, 79439, 135301, 229866, 389643, 659111, 1112833, 1875625, 3156219, 5303286, 8898709, 14912641, 24961201, 41734339, 69705889, 116311074, 193898159, 322961275
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OFFSET
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0,3
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COMMENTS
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This sequence is distantly related to (one-half) the number of losing strings using a binary alphabet in the "same game" described by Burns and Purcell (2007) and Kurz (2001). - Petros Hadjicostas, Sep 01 2019
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) for n > 5.
G.f.: (x^5 - x^4 - 2*x^3 + x^2 + x - 1)/((x - 1)*(x + 1)*(x^2 + x - 1)^2). (End)
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MATHEMATICA
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PROG
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(PARI) Vec((1 - x - x^2 + 2*x^3 + x^4 - x^5) / ((1 - x)*(1 + x)*(1 - x - x^2)^2) + O(x^40)) \\ Colin Barker, Mar 03 2019
(Magma) [n*Fibonacci(n)+((-1)^n+1)/2:n in [0..35]]; // Marius A. Burtea, Aug 29 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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