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A241749
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a(n) = n^2 + 13.
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2
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13, 14, 17, 22, 29, 38, 49, 62, 77, 94, 113, 134, 157, 182, 209, 238, 269, 302, 337, 374, 413, 454, 497, 542, 589, 638, 689, 742, 797, 854, 913, 974, 1037, 1102, 1169, 1238, 1309, 1382, 1457, 1534, 1613, 1694, 1777, 1862, 1949, 2038, 2129, 2222, 2317
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: (13 - 25*x + 14*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(13)*Pi*coth(sqrt(13)*Pi))/26.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(13)*Pi*cosech(sqrt(13)*Pi))/26. (End)
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MATHEMATICA
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Table[n^2 + 13, {n, 0, 60}]
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PROG
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(Magma) [n^2+13: 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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