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A024038
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a(n) = 4^n - n^2.
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2
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1, 3, 12, 55, 240, 999, 4060, 16335, 65472, 262063, 1048476, 4194183, 16777072, 67108695, 268435260, 1073741599, 4294967040, 17179868895, 68719476412, 274877906583, 1099511627376, 4398046510663, 17592186043932
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 - 4*x + 6*x^2 + 3*x^3)/((1 - x)^3*(1 - 4*x)). - Colin Barker, May 29 2012
E.g.f.: exp(4*x) - x*(1 + x)*exp(x). - G. C. Greubel, Aug 18 2023
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MATHEMATICA
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Table[4^n-n^2, {n, 0, 30}] (* or *) LinearRecurrence[{7, -15, 13, -4}, {1, 3, 12, 55}, 30] (* Harvey P. Dale, Sep 14 2013 *)
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PROG
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(SageMath) [4^n-n^2 for n in range(31)] # G. C. Greubel, Aug 18 2023
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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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