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A341841
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Square array T(n, k), n, k >= 0, read by antidiagonals upwards; for any number m with runs in binary expansion (r_1, ..., r_j), let R(m) = {r_1 + ... + r_j, r_2 + ... + r_j, ..., r_j}; T(n, k) is the unique number t such that R(t) equals R(n) minus R(k).
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3
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0, 1, 0, 2, 0, 0, 3, 3, 0, 0, 4, 3, 0, 1, 0, 5, 4, 0, 1, 1, 0, 6, 4, 7, 0, 1, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 8, 7, 7, 6, 0, 0, 3, 1, 0, 9, 8, 7, 6, 1, 0, 3, 2, 1, 0, 10, 8, 8, 7, 1, 0, 3, 3, 2, 0, 0, 11, 11, 8, 8, 0, 0, 3, 3, 3, 3, 0, 0, 12, 11, 8, 9, 15, 0, 0, 2, 3, 3, 0, 1, 0
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OFFSET
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0,4
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COMMENTS
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For any m > 0, R(m) contains the partial sums of the m-th row of A227736; by convention, R(0) = {}.
This sequence uses set subtraction, and is related to:
- A003987 which uses set difference,
- A341840 which uses set intersection.
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LINKS
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FORMULA
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T(n, n) = 0.
T(n, 0) = n.
T(T(n, k), k) = T(n, k).
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EXAMPLE
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Array T(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+--------------------------------------------------------------
0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1
2| 2 3 0 1 1 0 3 2 2 3 0 1 1 0 3 2
3| 3 3 0 0 0 0 3 3 3 3 0 0 0 0 3 3
4| 4 4 7 7 0 0 3 3 3 3 0 0 7 7 4 4
5| 5 4 7 6 1 0 3 2 2 3 0 1 6 7 4 5
6| 6 7 7 6 1 0 0 1 1 0 0 1 6 7 7 6
7| 7 7 7 7 0 0 0 0 0 0 0 0 7 7 7 7
8| 8 8 8 8 15 15 15 15 0 0 0 0 7 7 7 7
9| 9 8 8 9 14 15 15 14 1 0 0 1 6 7 7 6
10| 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5
11| 11 11 8 8 15 15 12 12 3 3 0 0 7 7 4 4
12| 12 12 15 15 15 15 12 12 3 3 0 0 0 0 3 3
13| 13 12 15 14 14 15 12 13 2 3 0 1 1 0 3 2
14| 14 15 15 14 14 15 15 14 1 0 0 1 1 0 0 1
15| 15 15 15 15 15 15 15 15 0 0 0 0 0 0 0 0
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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