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A131898
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a(n) = 2^(n+1) + 2*n - 1.
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3
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1, 5, 11, 21, 39, 73, 139, 269, 527, 1041, 2067, 4117, 8215, 16409, 32795, 65565, 131103, 262177, 524323, 1048613, 2097191, 4194345, 8388651, 16777261, 33554479, 67108913, 134217779, 268435509, 536870967, 1073741881, 2147483707, 4294967357, 8589934655, 17179869249
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OFFSET
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0,2
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COMMENTS
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Binomial transform of (1, 4, 2, 2, 2, ...).
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LINKS
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FORMULA
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G.f.: ( -1-x+4*x^2 ) / ( (2*x-1)*(x-1)^2 ). - R. J. Mathar, Jul 03 2011
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EXAMPLE
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a(3) = 21 = sum of row 3 terms of triangle A131897: (11 + 4 + 2 + 4).
a(3) = 21 = (1, 3, 3, 1) dot (1, 4, 2, 2) = (1 + 12 + 6 + 2).
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MATHEMATICA
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CoefficientList[Series[(-1-x+4*x^2)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)
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PROG
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(Magma) I:=[1, 5, 11]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 05 2012
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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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EXTENSIONS
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STATUS
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approved
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