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A259580 Sum of numbers in the n-th antidiagonal of the reciprocity array of 2. 3
2, 5, 8, 17, 30, 50, 78, 116, 162, 227, 300, 389, 498, 628, 766, 940, 1128, 1347, 1584, 1855, 2146, 2486, 2838, 3236, 3660, 4135, 4626, 5177, 5754, 6392, 7050, 7776, 8524, 9353, 10204, 11127, 12078, 13114, 14170, 15328, 16500, 17775, 19068, 20461, 21900 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..500

FORMULA

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

MATHEMATICA

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

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

CROSSREFS

Cf. A259572, A259578, A259579.

Sequence in context: A062318 A034445 A285459 * A316795 A054754 A054755

Adjacent sequences:  A259577 A259578 A259579 * A259581 A259582 A259583

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 17 2015

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)