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A241890
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a(n) = n^2 + 24.
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2
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24, 25, 28, 33, 40, 49, 60, 73, 88, 105, 124, 145, 168, 193, 220, 249, 280, 313, 348, 385, 424, 465, 508, 553, 600, 649, 700, 753, 808, 865, 924, 985, 1048, 1113, 1180, 1249, 1320, 1393, 1468, 1545, 1624, 1705, 1788, 1873, 1960, 2049, 2140, 2233, 2328
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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.: (24 - 47*x + 25*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(24)*Pi*coth(sqrt(24)*Pi))/48.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(24)*Pi*cosech(sqrt(24)*Pi))/48. (End)
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MATHEMATICA
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Table[n^2 + 24, {n, 0, 60}]
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PROG
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(Magma) [n^2+24: 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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