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A241851
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a(n) = n^2 + 21.
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3
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21, 22, 25, 30, 37, 46, 57, 70, 85, 102, 121, 142, 165, 190, 217, 246, 277, 310, 345, 382, 421, 462, 505, 550, 597, 646, 697, 750, 805, 862, 921, 982, 1045, 1110, 1177, 1246, 1317, 1390, 1465, 1542, 1621, 1702, 1785, 1870, 1957, 2046, 2137, 2230, 2325
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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.: (21 - 41*x + 22*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(21)*Pi*coth(sqrt(21)*Pi))/42.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(21)*Pi*cosech(sqrt(21)*Pi))/42. (End)
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MATHEMATICA
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Table[n^2 + 21, {n, 0, 60}]
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PROG
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(Magma) [n^2+21: n in [0..60]];
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CROSSREFS
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Cf. similar sequence 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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