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A218396
Number of compositions of n into distinct (nonzero) Fibonacci numbers.
9
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, Oct 28 2012
STATUS
approved