A240224 - OEIS

%I #7 May 08 2018 15:11:56

%S 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,

%T 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,

%U 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

%N 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.

%C The row length sequence is A240225. The number of partitions in row n is A000119(n).

%C 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.

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%e The array with separated partitions begins:

%e n\k       1         2          3         4            5 ...

%e 1:        1

%e 2:        2

%e 3:        3       2,1

%e 4:      3,1

%e 5:        5       3,2

%e 6:      5,1     3,2,1

%e 7:      5,2

%e 8:        8       5,3      5,2,1

%e 9:      8,1     5,3,1

%e 10:     8,2     5,3,2

%e 11:     8,3     8,2,1    5,3,2,1

%e 12:   8,3,1

%e 13:      13       8,5      8,3,2

%e 14:    13,1     8,5,1    8,3,2,1

%e 15:    13,2     8,5,2

%e 16:    13,3    13,2,1      8,5,3   8,5,2,1

%e 17:  13,3,1   8,5,3,1

%e 18:    13,5    13,3,2    8,5,3,2

%e 19:  13,5,1  13,3,2,1  8,5,3,2,1

%e 20:  13,5,2

%e 21:      21      13,8     13,5,3  13,5,2,1

%e 22:    21,1    13,8,1   13,5,3,1

%e 23:    21,2    13,8,2   13,5,3,2

%e 24:    21,3    21,2,1     13,8,3  13,8,2,1   13,5,3,2,1

%e 25:  21,3,1  13,8,3,1

%e ...

%Y Cf. A000119, A239001, A240225.

%K nonn,tabf

%O 1,2

%A _Wolfdieter Lang_, Apr 07 2014