A240224 - OEIS

A240224

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.

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

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..108.

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].

EXAMPLE

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

...

CROSSREFS

Cf. A000119, A239001, A240225.

Sequence in context: A373355 A270469 A204933 * A118105 A375301 A125211

Adjacent sequences: A240221 A240222 A240223 * A240225 A240226 A240227

KEYWORD

nonn,tabf

AUTHOR

Wolfdieter Lang, Apr 07 2014

STATUS

approved