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%I #19 Apr 06 2019 04:09:30
%S 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,
%T 10,11,12,13,12,13,14,15,14,13,14,15,14,13,14,15,14,15,16,17,16,15,16,
%U 17,16,15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,21,22,23,22,23
%N a(n) = Sum_{i=1..n} K(i,i+1), where K(x,y) is the Kronecker symbol (x/y).
%H G. C. Greubel, <a href="/A071933/b071933.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = n/4 + O(n), asymptotically. [Perhaps O(n) should be o(n)? - _N. J. A. Sloane_, Mar 26 2019]
%F 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
%t Table[Sum[KroneckerSymbol[j, j+1], {j, 1, n}], {n, 1, 80}] (* _G. C. Greubel_, Mar 17 2019 *)
%o (PARI) for(n=1,100,print1(sum(i=1,n,kronecker(i,i+1)),","))
%o (Sage) [sum(kronecker_symbol(j,j+1) for j in (1..n)) for n in (1..80)] # _G. C. Greubel_, Mar 17 2019
%Y Cf. A071932, A071934.
%K easy,nonn
%O 1,4
%A _Benoit Cloitre_, Jun 14 2002