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A135165
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a(n) = 7^n + 5^n - 3^n - 2^n.
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1
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0, 7, 61, 433, 2929, 19657, 132481, 899353, 6148609, 42286537, 292180801, 2025975673, 14084892289, 98108111017, 684321789121, 4778064706393, 33385475347969, 233393324169097, 1632227907493441, 11417967508915513, 79887630241419649, 559022690779036777, 3912205202988749761
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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) = 2929 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401+625-81-16 = 2929.
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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, 7, 61, 433}, 30] (* Harvey P. Dale, Mar 20 2015 *)
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PROG
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(Magma) I:=[0, 7, 61, 433]; [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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STATUS
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approved
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