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Search: id:A081946
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| A081946 |
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a(n) = sum(i=1,n,floor(r*floor(i/r))) where r=sqrt(2). |
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+0
1
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| 0, 1, 3, 5, 9, 14, 19, 26, 34, 43, 52, 63, 75, 87, 101, 116, 132, 148, 166, 185, 204, 225, 247, 269, 293, 318, 344, 370, 398, 427, 456, 487, 519, 552, 585, 620, 656, 692, 730, 769, 808, 849, 891, 934, 977, 1022, 1068, 1114, 1162, 1211, 1261, 1311, 1363, 1416
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OFFSET
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1,3
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COMMENT
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More generally if r is irrational 1<r<2 then : sum(i=1,n,floor(r*floor(i/r))) = n*(n+1)/2-floor((1-1/r)*n); if r>2, there is the asymptotic formula : sum(i=1,n,floor(r*floor(i/r))) = n*(n+1)/2-ceil(r)*(1-floor(r)/2/r)*n + O(1)
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FORMULA
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a(n) = n*(n+1)/2-floor((1-1/sqrt(2))*n)
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CROSSREFS
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Adjacent sequences: A081943 A081944 A081945 this_sequence A081947 A081948 A081949
Sequence in context: A118002 A069533 A054066 this_sequence A053618 A032801 A033818
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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), Jun 13 2003
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