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

0,4

Links

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

Example

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.

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).

Sequence in context: A226469 A073341 A227470 * A368154 A331926 A070982

Adjacent sequences: A218393 A218394 A218395 * A218397 A218398 A218399

Keyword

nonn

Author

Joerg Arndt, Oct 28 2012

Status

approved