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A086341
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a(n) = 2*2^floor(n/2) - (-1)^n.
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5
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1, 3, 3, 5, 7, 9, 15, 17, 31, 33, 63, 65, 127, 129, 255, 257, 511, 513, 1023, 1025, 2047, 2049, 4095, 4097, 8191, 8193, 16383, 16385, 32767, 32769, 65535, 65537, 131071, 131073, 262143, 262145, 524287, 524289, 1048575, 1048577, 2097151, 2097153
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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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E.g.f.: 2*cosh(sqrt(2)*x) + 2*sinh(sqrt(2)*x)/sqrt(2) - sinh(x) + cosh(x).
a(n) = (1 + 1/sqrt(2))*sqrt(2)^n + (1 - 1/sqrt(2))*(-sqrt(2))^n - (-1)^n.
G.f.: (1+2*x)^2/((1+x)*(1-2*x^2)). - Colin Barker, Aug 17 2012
a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3); a(0)=1, a(1)=3, a(2)=3. - Harvey P. Dale, Mar 10 2013
Sum_{n>=0} (-1)^n/a(n) = 2 * A248721. (End)
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MATHEMATICA
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CoefficientList[Series[(1+2x)^2/((1+x)(1-2x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[ {-1, 2, 2}, {1, 3, 3}, 50] (* Harvey P. Dale, Mar 10 2013 *)
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PROG
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(PARI) vector(40, n, n--; 2^(floor(n/2)+1) - (-1)^n) \\ G. C. Greubel, Nov 08 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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