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A259580 Sum of numbers in the n-th antidiagonal of the reciprocity array of 2. 3

%I

%S 2,5,8,17,30,50,78,116,162,227,300,389,498,628,766,940,1128,1347,1584,

%T 1855,2146,2486,2838,3236,3660,4135,4626,5177,5754,6392,7050,7776,

%U 8524,9353,10204,11127,12078,13114,14170,15328,16500,17775,19068,20461,21900

%N Sum of numbers in the n-th antidiagonal of the reciprocity array of 2.

%C The "reciprocity law" that Sum{[(n*k+x)/m] : k = 0..m} = Sum{[(m*k+x)/n] : k = 0..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 R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, 1989, pages 90-94.

%H Clark Kimberling, <a href="/A259580/b259580.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = Sum_{m=1..n} Sum_{k=0..m-1} floor((n*k + x)/m), where x = 2.

%t x = 2; v[n_] := Sum[Sum[Floor[(n*k + x)/m], {k, 0, m - 1}], {m, 1, n}];

%t Table[v[n], {n, 1, 120}]

%Y Cf. A259572, A259578, A259579.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 17 2015

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)