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A071933
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a(n) = Sum_{i=1..n} K(i,i+1), where K(x,y) is the Kronecker symbol (x/y).
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3
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1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 8, 9, 8, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 13, 14, 15, 14, 13, 14, 15, 14, 15, 16, 17, 16, 15, 16, 17, 16, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 21, 22, 23, 22, 23
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = n/4 + O(n), asymptotically. [Perhaps O(n) should be o(n)? - N. J. A. Sloane, Mar 26 2019]
In fact we have a(n) = n/4 + O(log(n)). More precisely let c(n)=A037800(n) then we get a(8n)=2n+2+2c(n), a(8n+1)=2n+3+2c(n), a(8n+2)=2n+2+2c(n), a(8n+3)=2n+2+2c(n)+(-1)^n, a(8n+4)=2n+3+2c(n)+(-1)^n, a(8n+5)=2n+4+2c(n)+(-1)^n, a(8n+6)=2n+3+2c(n)+(-1)^n, a(8n+7)=2n+3+2c(n+1). - Benoit Cloitre, Mar 30 2019
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MATHEMATICA
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Table[Sum[KroneckerSymbol[j, j+1], {j, 1, n}], {n, 1, 80}] (* G. C. Greubel, Mar 17 2019 *)
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PROG
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(PARI) for(n=1, 100, print1(sum(i=1, n, kronecker(i, i+1)), ", "))
(Sage) [sum(kronecker_symbol(j, j+1) for j in (1..n)) for n in (1..80)] # G. C. Greubel, Mar 17 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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