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A065532
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a(n) = 48*n^2 - 1.
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2
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-1, 47, 191, 431, 767, 1199, 1727, 2351, 3071, 3887, 4799, 5807, 6911, 8111, 9407, 10799, 12287, 13871, 15551, 17327, 19199, 21167, 23231, 25391, 27647, 29999, 32447, 34991, 37631, 40367, 43199, 46127, 49151, 52271, 55487, 58799, 62207, 65711, 69311, 73007, 76799
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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 - 50*x - 47*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)) - 1)/2. (End)
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MATHEMATICA
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CoefficientList[Series[(1-50*x-47*x^2)/(x-1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3, -3, 1}, {-1, 47, 191}, 40] (* Harvey P. Dale, Dec 13 2017 *)
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PROG
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(PARI) { for (n=0, 1000, write("b065532.txt", n, " ", 48*n^2 - 1) ) } \\ Harry J. Smith, Oct 21 2009
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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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