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A135163
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a(n) = 7^n - 5^n + 3^n - 2^n.
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1
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0, 3, 29, 237, 1841, 13893, 102689, 747477, 5380481, 38419653, 272767649, 1928673717, 13597673921, 95669893413, 672124323809, 4717058247957, 33080385660161, 231867703543173, 1624599287803169, 11379822860782197, 79696902351707201, 558069037383336933, 3907436894168837729
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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) = 7^n - 5^n + 3^n - 2^n.
G.f.: 1/(1-7*x) - 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)
E.g.f.: exp(7*x) - exp(5*x) + exp(3*x) - exp(2*x). - G. C. Greubel, Sep 30 2016
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EXAMPLE
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a(4) = 1841 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81-16 = 1841.
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MATHEMATICA
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CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) + 1/(1 - 3 x) - 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
LinearRecurrence[{17, -101, 247, -210}, {0, 3, 29, 237}, 30] (* Harvey P. Dale, Sep 17 2016 *)
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PROG
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(Magma) I:=[0, 3, 29, 237]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 22 2014
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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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