This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259580 #11 Mar 03 2025 06:48:11
%S A259580 2,5,8,17,30,50,78,116,162,227,300,389,498,628,766,940,1128,1347,1584,
%T A259580 1855,2146,2486,2838,3236,3660,4135,4626,5177,5754,6392,7050,7776,
%U A259580 8524,9353,10204,11127,12078,13114,14170,15328,16500,17775,19068,20461,21900
%N A259580 Sum of numbers in the n-th antidiagonal of the reciprocity array of 2.
%C A259580 The "reciprocity law" that Sum_{k=0..m} [(n*k+x)/m] = Sum_{k=0..n} [(m*k+x)/n] where x is a real number and m and n are positive integers, is proved in Section 3.5 of Concrete Mathematics (see References). See A259572 for a guide to related sequences.
%D A259580 R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, 1989, pages 90-94.
%H A259580 Clark Kimberling, <a href="/A259580/b259580.txt">Table of n, a(n) for n = 1..500</a>
%F A259580 a(n) = Sum_{m=1..n} Sum_{k=0..m-1} floor((n*k + x)/m), where x = 2.
%t A259580 x = 2; v[n_] := Sum[Sum[Floor[(n*k + x)/m], {k, 0, m - 1}], {m, 1, n}];
%t A259580 Table[v[n], {n, 1, 120}]
%Y A259580 Cf. A259572, A259578, A259579.
%K A259580 nonn,easy
%O A259580 1,1
%A A259580 _Clark Kimberling_, Jul 17 2015