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%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
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