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%I #4 Jul 15 2015 17:32:35
%S 3,6,13,19,34,55,84,120,174,231,310,399,510,634,786,948,1144,1359,
%T 1602,1863,2176,2496,2860,3256,3680,4147,4662,5189,5782,6412,7080,
%U 7792,8574,9369,10228,11151,12114,13132,14230,15344,16540,17805,19110,20481,21948
%N Sum of numbers in the n-th antidiagonal of the reciprocity array of 3.
%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,
%C 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="/A259583/b259583.txt">Table of n, a(n) for n = 1..499</a>
%F a(n) = sum{sum{floor((n*k + x)/m), k=0..m-1, m=1..n}, where x = 3.
%t x = 3; 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, A259581, A259582.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jul 15 2015
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