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A093112
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a(n) = (2^n-1)^2 - 2.
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7
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-1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023, 67092479, 268402687, 1073676287, 4294836223, 17179607039, 68718952447, 274876858367, 1099509530623, 4398042316799, 17592177655807, 70368727400447, 281474943156223, 1125899839733759
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OFFSET
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1,2
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COMMENTS
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Cletus Emmanuel calls these "Carol numbers".
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LINKS
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FORMULA
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a(n) = (2^n-1)^2 - 2.
a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3) + 8*a(n-4).
G.f.: x*(16*x^2-14*x+1) / ((x-1)*(2*x-1)*(4*x-1)). (End)
E.g.f.: 2 - exp(x) - 2*exp(2*x) + exp(4*x). - Stefano Spezia, Dec 09 2019
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MAPLE
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MATHEMATICA
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Rest@ CoefficientList[Series[x (16 x^2 - 14 x + 1)/((x - 1) (2 x - 1) (4 x - 1)), {x, 0, 25}], x] (* Michael De Vlieger, Dec 09 2019 *)
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PROG
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(PARI) Vec(x*(16*x^2-14*x+1)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 07 2014
(Python)
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CROSSREFS
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KEYWORD
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sign,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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