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A255845
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a(n) = 2*n^2 + 10.
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1
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10, 12, 18, 28, 42, 60, 82, 108, 138, 172, 210, 252, 298, 348, 402, 460, 522, 588, 658, 732, 810, 892, 978, 1068, 1162, 1260, 1362, 1468, 1578, 1692, 1810, 1932, 2058, 2188, 2322, 2460, 2602, 2748, 2898, 3052, 3210, 3372, 3538, 3708, 3882, 4060, 4242, 4428
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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=5 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
Equivalently, numbers m such that 2*m - 20 is a square.
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LINKS
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FORMULA
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G.f.: 2*(5 - 9*x + 6*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=0} 1/a(n) = (1 + sqrt(5)*Pi*coth(sqrt(5)*Pi))/20.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(5)*Pi*cosech(sqrt(5)*Pi))/20. (End)
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MATHEMATICA
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Table[2 n^2 + 10, {n, 0, 50}]
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PROG
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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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