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A306534
Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Sum_{j=0..n} floor(n/k^j).
1
0, 0, 2, 0, 1, 6, 0, 1, 3, 12, 0, 1, 2, 4, 20, 0, 1, 2, 4, 7, 30, 0, 1, 2, 3, 5, 8, 42, 0, 1, 2, 3, 5, 6, 10, 56, 0, 1, 2, 3, 4, 6, 8, 11, 72, 0, 1, 2, 3, 4, 6, 7, 9, 15, 90, 0, 1, 2, 3, 4, 5, 7, 8, 10, 16, 110, 0, 1, 2, 3, 4, 5, 7, 8, 10, 13, 18, 132, 0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 19, 156
OFFSET
0,3
FORMULA
G.f. of column k (for k > 1): (1/(1 - x)) * Sum_{j>=0} x^(k^j)/(1 - x^(k^j)).
EXAMPLE
Square array begins:
0, 0, 0, 0, 0, 0, ...
2, 1, 1, 1, 1, 1, ...
6, 3, 2, 2, 2, 2, ...
12, 4, 4, 3, 3, 3, ...
20, 7, 5, 5, 4, 4, ...
30, 8, 6, 6, 6, 5, ...
MATHEMATICA
Table[Function[k, Sum[Floor[n/k^j], {j, 0, n}]][i - n + 1], {i, 0, 12}, {n, 0, i}] // Flatten
CROSSREFS
Columns k=1..4 give A002378, A005187, A004128, A087069.
Cf. A306533.
Sequence in context: A338774 A330891 A089627 * A344392 A331787 A321686
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Feb 22 2019
STATUS
approved