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A135159
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a(n) = 5^n - 3^n + 2^n.
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9
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1, 4, 20, 106, 560, 2914, 14960, 76066, 384320, 1933954, 9707600, 48653026, 243613280, 1219116994, 6098749040, 30503261986, 152544909440, 762810444034, 3814310107280, 19072324590946, 95363945904800, 476826699947074, 2384154414150320, 11920834820287906, 59604362362631360, 298022376621898114
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OFFSET
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0,2
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COMMENTS
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Constants are the prime numbers in decreasing order.
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LINKS
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FORMULA
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a(n) = 5^n - 3^n + 2^n.
G.f.: 1/(1-5*x) - 1/(1-3*x) + 1/(1-2*x).
E.g.f.: exp(5*x) - exp(3*x) + exp(2*x). (End)
a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - G. C. Greubel, Sep 30 2016
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EXAMPLE
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a(4)=560 because 5^4=625, 3^4=81, 2^4=16 and 625-81+16=560.
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MATHEMATICA
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CoefficientList[Series[1/(1 - 5 x) - 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
Table[5^n - 3^n + 2^n, {n, 0, 25}] (* or *) LinearRecurrence[{10, -31, 30}, {1, 4, 20}, 25] (* G. C. Greubel, Sep 30 2016 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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