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A356325
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Array A(n, k), n, k >= 0, read by antidiagonals; the terms in the negaFibonacci representation of A(n, k) are the terms in common in the negaFibonacci representations of n and k.
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3
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0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 2, 1, 5, 5, 1, 2, 1, 0, 0, 0, 2, 2, 5, 5, 5, 2, 2, 0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 3, 0, 0, 0, 0, 1, 0, 0, 5, 5, 6, 5, 5, 0, 0, 1, 0
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OFFSET
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0,13
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COMMENTS
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This sequence has similarities with A334348.
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LINKS
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FORMULA
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A(n, k) = A(k, n).
A(n, n) = n.
A(n, 0) = 0.
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EXAMPLE
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Array A(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
---+------------------------------------------------
0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1| 0 1 0 1 0 0 1 0 1 0 0 1 0 0
2| 0 0 2 2 0 0 0 2 2 0 0 0 0 0
3| 0 1 2 3 0 0 1 2 3 0 0 1 0 0
4| 0 0 0 0 4 5 5 5 5 -1 0 0 -1 0
5| 0 0 0 0 5 5 5 5 5 0 0 0 0 0
6| 0 1 0 1 5 5 6 5 6 0 0 1 0 0
7| 0 0 2 2 5 5 5 7 7 0 0 0 0 0
8| 0 1 2 3 5 5 6 7 8 0 0 1 0 0
9| 0 0 0 0 -1 0 0 0 0 9 10 10 12 13
10| 0 0 0 0 0 0 0 0 0 10 10 10 13 13
11| 0 1 0 1 0 0 1 0 1 10 10 11 13 13
12| 0 0 0 0 -1 0 0 0 0 12 13 13 12 13
13| 0 0 0 0 0 0 0 0 0 13 13 13 13 13
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For n = 14 and k = 43:
- 14 = F(-1) + F(-7),
- 43 = F(-2) + F(-4) + F(-7) + F(-9),
- so A(14, 43) = F(-7) = 13.
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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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