A218396 Number of compositions of n into distinct (nonzero) Fibonacci numbers.

1, 1, 1, 3, 2, 3, 8, 2, 9, 8, 8, 32, 6, 9, 32, 8, 38, 30, 32, 150, 6, 33, 32, 32, 158, 30, 38, 174, 30, 176, 150, 150, 870, 24, 33, 152, 32, 182, 150, 158, 894, 30, 182, 174, 174, 1014, 144, 176, 990, 150, 1014, 864, 870, 5904, 24, 153, 152, 152, 902, 150, 182, 1014, 150, 1022, 894, 894, 6054, 144

Offset: 0

Author

Joerg Arndt, Oct 28 2012

Keywords

• nonn

Examples

			There are a(37)=182 such compositions of 37. Each of the 6 partitions of 37 into distinct Fibonacci numbers corresponds to m! compositions (where m is the number of parts):
  #:  partition      ( m! compositions)
  1:  1 2 5 8 21     (120 compositions)
  2:  1 2 13 21      ( 24 compositions)
  3:  1 2 34         (  6 compositions)
  4:  3 5 8 21       ( 24 compositions)
  5:  3 13 21        (  6 compositions)
  6:  3 34           (  2 compositions)
The number of compositions is 120 + 24 + 6 + 24 + 6 + 2 = 182.
		

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms 0..200 from Joerg Arndt)

Crossrefs

Cf. A032021 (compositions into distinct odd numbers).

Cf. A000119 (partitions into distinct nonzero Fibonacci numbers), A000700 (partitions into distinct odd numbers).

Cf. A076739 (compositions into Fibonacci numbers).