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A241849
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a(n) = n^2 + 19.
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2
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19, 20, 23, 28, 35, 44, 55, 68, 83, 100, 119, 140, 163, 188, 215, 244, 275, 308, 343, 380, 419, 460, 503, 548, 595, 644, 695, 748, 803, 860, 919, 980, 1043, 1108, 1175, 1244, 1315, 1388, 1463, 1540, 1619, 1700, 1783, 1868, 1955, 2044, 2135, 2228, 2323
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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.: (19 - 37*x + 20*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(19)*Pi*coth(sqrt(19)*Pi))/38.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End)
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MAPLE
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MATHEMATICA
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Table[n^2 + 19, {n, 0, 60}]
LinearRecurrence[{3, -3, 1}, {19, 20, 23}, 50] (* Harvey P. Dale, Dec 05 2018 *)
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PROG
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(Magma) [n^2+19: 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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