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Search: id:A076644
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| A076644 |
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a(1)=1; for n>1, a(n) = a(n-floor(sqrt(n))) + n. |
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3
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| 1, 3, 6, 7, 11, 13, 18, 21, 22, 28, 32, 34, 41, 46, 49, 50, 58, 64, 68, 70, 79, 86, 91, 94, 95, 105, 113, 119, 123, 125, 136, 145, 152, 157, 160, 161, 173, 183, 191, 197, 201, 203, 216, 227, 236, 243, 248, 251, 252, 266, 278, 288, 296, 302, 306, 308, 323, 336
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = floor(2/3*n*(sqrt(n)+1)) for n=1,2,4,6,17,24,26,29,43,83,88,193,207,243,357,534,806,1082,1197,1377... Sign of a(n) - floor(2/3*n*(sqrt(n)+1)) changes often.
Cumulative sums of A122196. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 25 2006
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FORMULA
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Write n=r^2+s with -r < s <= r; then a(n) = r(r+1)(4r-1)/6 + x, where x = -s^2 if s <= 0, x = s(2r+1-s) if s >= 0. - Dean Hickerson (dean(AT)math.ucdavis.edu), Nov 11 2002
a(n) is asymptotic to 2/3*n^(3/2).
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MATHEMATICA
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a[n_] := Module[{r, s}, r=Floor[1/2+Sqrt[n]]; s=n-r^2; (r(r+1)(4r-1))/6+If[s<=0, -s^2, s(2r+1-s)]]
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PROGRAM
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(PARI) a(n)=if(n<2, n>0, n+a(n-sqrtint(n)))
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CROSSREFS
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Cf. A122196.
Sequence in context: A091067 A120511 A022550 this_sequence A087642 A084349 A126003
Adjacent sequences: A076641 A076642 A076643 this_sequence A076645 A076646 A076647
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2002
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