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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
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 15 2015
STATUS
approved