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A255846
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a(n) = 2*n^2 + 14.
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1
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14, 16, 22, 32, 46, 64, 86, 112, 142, 176, 214, 256, 302, 352, 406, 464, 526, 592, 662, 736, 814, 896, 982, 1072, 1166, 1264, 1366, 1472, 1582, 1696, 1814, 1936, 2062, 2192, 2326, 2464, 2606, 2752, 2902, 3056, 3214, 3376, 3542, 3712, 3886, 4064, 4246, 4432
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OFFSET
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0,1
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COMMENTS
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This is the case k=7 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
Equivalently, numbers m such that 2*m - 28 is a square.
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LINKS
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FORMULA
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G.f.: 2*(7 - 13*x + 8*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = (1 + sqrt(7)*Pi*coth(sqrt(7)*Pi))/28.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(7)*Pi*cosech(sqrt(7)*Pi))/28. (End)
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MATHEMATICA
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Table[2 n^2 + 14, {n, 0, 50}]
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PROG
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(PARI) vector(50, n, n--; 2*n^2+14)
(Sage) [2*n^2+14 for n in (0..50)]
(Magma) [2*n^2+14: n in [0..50]];
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CROSSREFS
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Cf. similar sequences listed in A255843.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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