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A135167
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a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order.
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2
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2, 13, 79, 487, 3091, 20143, 133939, 903727, 6161731, 42325903, 292298899, 2026329967, 14085955171, 98111299663, 684331355059, 4778093404207, 33385561441411, 233393582449423, 1632228682334419, 11417969833438447, 79887637214988451, 559022711699743183, 3912205265750868979
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = 7^n + 5^n + 3^n - 2^n.
a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).
G.f.: (2 - 21*x + 60*x^2 - 37*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).
E.g.f.: exp(7*x) + exp(5*x) + exp(3*x) - exp(2*x). (End)
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EXAMPLE
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a(4)=3091 because 7^4=2401, 5^4=625, 3^4=81, 2^4=16 and we can write 2401+625+81-16=3091.
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MATHEMATICA
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Table[7^n + 5^n + 3^n - 2^n, {n, 0, 50}] (* or *) LinearRecurrence[{17, -101, 247, -210}, {2, 13, 79, 487}, 50] (* 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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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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