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A240224
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Irregular triangular array read by rows: row n gives a list of the partitions of n into distinct Fibonacci numbers. The order of the partitions is like in Abramowitz-Stegun.
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1
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1, 2, 3, 2, 1, 3, 1, 5, 3, 2, 5, 1, 3, 2, 1, 5, 2, 8, 5, 3, 5, 2, 1, 8, 1, 5, 3, 1, 8, 2, 5, 3, 2, 8, 3, 8, 2, 1, 5, 3, 2, 1, 8, 3, 1, 13, 8, 5, 8, 3, 2, 13, 1, 8, 5, 1, 8, 3, 2, 1, 13, 2, 8, 5, 2, 13, 3, 13, 2, 1, 8, 5, 3, 8, 5, 2, 1, 13, 3, 1, 8, 5, 3, 1, 13, 5, 13, 3, 2, 8, 5, 3, 2, 13, 5, 1, 13, 3, 2, 1, 8, 5, 3, 2, 1, 13, 5, 2
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OFFSET
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1,2
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COMMENTS
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The row length sequence is A240225. The number of partitions in row n is A000119(n).
The order of the partitions is like in Abramowitz-Stegun (rising number of parts, within like part numbers lexicographic) but here the order of the parts has been reversed, that is they are ordered decreasingly.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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The array with separated partitions begins:
n\k 1 2 3 4 5 ...
1: 1
2: 2
3: 3 2,1
4: 3,1
5: 5 3,2
6: 5,1 3,2,1
7: 5,2
8: 8 5,3 5,2,1
9: 8,1 5,3,1
10: 8,2 5,3,2
11: 8,3 8,2,1 5,3,2,1
12: 8,3,1
13: 13 8,5 8,3,2
14: 13,1 8,5,1 8,3,2,1
15: 13,2 8,5,2
16: 13,3 13,2,1 8,5,3 8,5,2,1
17: 13,3,1 8,5,3,1
18: 13,5 13,3,2 8,5,3,2
19: 13,5,1 13,3,2,1 8,5,3,2,1
20: 13,5,2
21: 21 13,8 13,5,3 13,5,2,1
22: 21,1 13,8,1 13,5,3,1
23: 21,2 13,8,2 13,5,3,2
24: 21,3 21,2,1 13,8,3 13,8,2,1 13,5,3,2,1
25: 21,3,1 13,8,3,1
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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