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A241750
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a(n) = n^2 + 15.
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2
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15, 16, 19, 24, 31, 40, 51, 64, 79, 96, 115, 136, 159, 184, 211, 240, 271, 304, 339, 376, 415, 456, 499, 544, 591, 640, 691, 744, 799, 856, 915, 976, 1039, 1104, 1171, 1240, 1311, 1384, 1459, 1536, 1615, 1696, 1779, 1864, 1951, 2040, 2131, 2224, 2319
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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.: (15 - 29*x + 16*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(15)*Pi*coth(sqrt(15)*Pi))/30.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(15)*Pi*cosech(sqrt(15)*Pi))/30. (End)
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MATHEMATICA
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Table[n^2 + 15, {n, 0, 60}]
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PROG
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(Magma) [n^2+15: 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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