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A212649
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a(n) = floor(sum_{k, 0 <= k <= n-1} sqrt(n^2 - k^2)).
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0
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1, 3, 8, 13, 21, 30, 41, 53, 67, 82, 99, 118, 138, 159, 183, 207, 234, 262, 291, 322, 355, 389, 425, 462, 501, 542, 584, 628, 673, 720, 768, 818, 870, 923, 977, 1034, 1091, 1151, 1212, 1274, 1338, 1404, 1471, 1540, 1610, 1682, 1756, 1831, 1908, 1986, 2066
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OFFSET
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1,2
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COMMENTS
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a(n)/n^2 converges to pi/4 = 0.78539816... when n tends to infinity.
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LINKS
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FORMULA
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a(n) = Floor(sum_{k, 0<=k<=n-1} sqrt(A094728(n,k))).
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EXAMPLE
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A094728(4) is {16, 15, 12, 7). Hence, a(4) = floor(sqrt(16) + sqrt(15) + sqrt(12) + sqrt(7)) = floor(13.9828...) = 13.
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MATHEMATICA
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Table[Floor[Sum[Sqrt[n^2 - k^2], {k, 0, n - 1}]], {n, 60}] (* T. D. Noe, Mar 19 2013 *)
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CROSSREFS
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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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