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Search: id:A022554
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| A022554 |
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Sum [ sqrt(k) ], k=0..n. |
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+0
1
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| 0, 1, 2, 3, 5, 7, 9, 11, 13, 16, 19, 22, 25, 28, 31, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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D.E. Knuth, The art of programming, Vol. 1, 3rd Edition, Addison-Wesley, 1997, Ex. 43 of section 1.2.4.
M. Griffiths, More sums involving the floor function, Math. Gaz., 86 (2002), 285-287.
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FORMULA
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a(0)=0, a(1)=1; a(n) = 2 a(n-1) - a(n-2) if n is not a perfect square; a(n) = 2 a(n-1) - a(n-2) + 1 if n is a perfect square.
a(n) = floor(sqrt(n)) * (n-1/6*(2*floor(sqrt(n))+5)*(floor(sqrt(n))-1)) - Yong Kong (ykong(AT)curagen.com), Mar 10 2001
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MAPLE
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Sum(floor(sqrt(k)), k=0..n)
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CROSSREFS
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Sequence in context: A129895 A096149 A033055 this_sequence A097046 A011861 A065520
Adjacent sequences: A022551 A022552 A022553 this_sequence A022555 A022556 A022557
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KEYWORD
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nonn,easy
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AUTHOR
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Michel Tixier (tixier(AT)dyadel.net)
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EXTENSIONS
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More terms from Yong Kong (ykong(AT)curagen.com), Mar 10 2001
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