OFFSET
1,2
COMMENTS
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.
REFERENCES
R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, 1989, pages 90-94.
EXAMPLE
In the array at A259581, row 4 is (3,4,6,6,9,10,12,12,15,16,...), with differences (1,2,0,3,1,2,2,3,1,...),
and distinct differences {0,1,2,3}, so that a(4) = 4.
MATHEMATICA
x = 3; s[m_, n_] := Sum[Floor[(n*k + x)/m], {k, 0, m - 1}];
t[m_] := Table[s[m, n], {n, 1, 1000}];
Table[Length[Union[Differences[t[m]]]], {m, 1, 120}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 15 2015
STATUS
approved