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A001589
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a(n) = 4^n + n^4.
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12
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1, 5, 32, 145, 512, 1649, 5392, 18785, 69632, 268705, 1058576, 4208945, 16797952, 67137425, 268473872, 1073792449, 4295032832, 17179952705, 68719581712, 274878037265, 1099511787776, 4398046705585, 17592186278672
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OFFSET
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0,2
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COMMENTS
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The statement above (and the corollary that 5 is the only prime term in this sequence) can be proved using Sophie Germain's identity x^4 + 4y^4 = (x^2 + 2xy + 2y^2)(x^2 - 2xy + 2y^2). - Alonso del Arte, Oct 31 2013 [exponents corrected by Thomas Ordowski, Nov 29 2017]
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LINKS
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FORMULA
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G.f.: -(5*x^5 + 38*x^4 + 43*x^3 - 17*x^2 + 4*x - 1) / ((x - 1)^5*(4*x - 1)). - Colin Barker, Jan 01 2013
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MATHEMATICA
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LinearRecurrence[{9, -30, 50, -45, 21, -4}, {1, 5, 32, 145, 512, 1649}, 30] (* Harvey P. Dale, Mar 06 2023 *)
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PROG
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(PARI) a(n)=1<<(n+n)+n^4
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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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