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A259583 Sum of numbers in the n-th antidiagonal of the reciprocity array of 3. 3
3, 6, 13, 19, 34, 55, 84, 120, 174, 231, 310, 399, 510, 634, 786, 948, 1144, 1359, 1602, 1863, 2176, 2496, 2860, 3256, 3680, 4147, 4662, 5189, 5782, 6412, 7080, 7792, 8574, 9369, 10228, 11151, 12114, 13132, 14230, 15344, 16540, 17805, 19110, 20481, 21948 (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..499

FORMULA

a(n) = sum{sum{floor((n*k + x)/m), k=0..m-1, m=1..n}, where x = 3.

MATHEMATICA

x = 3;  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, A259581, A259582.

Sequence in context: A137042 A080546 A080554 * A064349 A101965 A230370

Adjacent sequences:  A259580 A259581 A259582 * A259584 A259585 A259586

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 15 2015

STATUS

approved

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Last modified June 23 21:29 EDT 2017. Contains 288675 sequences.