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A361789
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A(n, k) is the sum of the distinct terms in the dual Zeckendorf representations of n or of k; square array A(n, k) read by antidiagonals, n, k >= 0.
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1
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0, 1, 1, 2, 1, 2, 3, 3, 3, 3, 4, 3, 2, 3, 4, 5, 4, 3, 3, 4, 5, 6, 6, 6, 3, 6, 6, 6, 7, 6, 5, 6, 6, 5, 6, 7, 8, 8, 6, 6, 4, 6, 6, 8, 8, 9, 8, 7, 6, 6, 6, 6, 7, 8, 9, 10, 9, 8, 8, 6, 5, 6, 8, 8, 9, 10, 11, 11, 11, 8, 11, 6, 6, 11, 8, 11, 11, 11, 12, 11, 10, 11, 11, 10, 6, 10, 11, 11, 10, 11, 12
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OFFSET
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0,4
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COMMENTS
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The dual Zeckendorf representation corresponds to the lazy Fibonacci representation (see A356771 for further details).
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LINKS
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FORMULA
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A(n, k) = A(k, n).
A(n, 0) = n.
A(n, n) = n.
A(A(m, n), k) = A(m, A(n, k)).
A(A(n, k), n) = A(n, k).
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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 1 2 3 4 5 6 7 8 9 10 11 12 13
1 | 1 1 3 3 4 6 6 8 8 9 11 11 12 14
2 | 2 3 2 3 6 5 6 7 8 11 10 11 14 13
3 | 3 3 3 3 6 6 6 8 8 11 11 11 14 14
4 | 4 4 6 6 4 6 6 11 11 9 11 11 12 14
5 | 5 6 5 6 6 5 6 10 11 11 10 11 14 13
6 | 6 6 6 6 6 6 6 11 11 11 11 11 14 14
7 | 7 8 7 8 11 10 11 7 8 11 10 11 19 18
8 | 8 8 8 8 11 11 11 8 8 11 11 11 19 19
9 | 9 9 11 11 9 11 11 11 11 9 11 11 17 19
10 | 10 11 10 11 11 10 11 10 11 11 10 11 19 18
11 | 11 11 11 11 11 11 11 11 11 11 11 11 19 19
12 | 12 12 14 14 12 14 14 19 19 17 19 19 12 14
13 | 13 14 13 14 14 13 14 18 19 19 18 19 14 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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