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A241889
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a(n) = n^2 + 23.
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2
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23, 24, 27, 32, 39, 48, 59, 72, 87, 104, 123, 144, 167, 192, 219, 248, 279, 312, 347, 384, 423, 464, 507, 552, 599, 648, 699, 752, 807, 864, 923, 984, 1047, 1112, 1179, 1248, 1319, 1392, 1467, 1544, 1623, 1704, 1787, 1872, 1959, 2048, 2139, 2232, 2327
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (23 - 45*x + 24*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
Sum_{n>=0} 1/a(n) = (1 + sqrt(23)*Pi*coth(sqrt(23)*Pi))/46.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(23)*Pi*cosech(sqrt(23)*Pi))/46. (End)
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MATHEMATICA
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CoefficientList[Series[(23 - 45 x + 24 x^2)/(1 - x)^3, {x, 0, 60}], x]
Range[0, 50]^2 + 23 (* or *) LinearRecurrence[{3, -3, 1}, {23, 24, 27}, 50] (* Harvey P. Dale, May 27 2014 *)
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PROG
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(Magma) [n^2+23: n in [0..60]];
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CROSSREFS
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Cf. similar sequences listed in A114962.
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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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