OFFSET
0,4
COMMENTS
The standard order of compositions is given by A066099.
Number of ways to distribute labeled objects into boxes, with the number of objects in each box being specified by the composition.
LINKS
Alois P. Heinz, Rows n = 0..14, flattened
Thomas Garrity and Jacob Lehmann Duke, Ergodicity and Algebraticity of the Fast and Slow Triangle Maps, arXiv:2409.05822 [math.DS], 2024. See p. 22.
FORMULA
For composition b(1),...,b(k), a(n) = (Sum_{i=1}^k b(i))! / (Product_{i=1}^k b(i)!).
EXAMPLE
Composition number 11 is 2,1,1; there are 6 choices for the pair of objects in the first box, then 2 choices for the object in the next box, so a(11) = 6*2 = 12.
The table starts:
1
1
1 2
1 3 3 6
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Franklin T. Adams-Watters, Nov 06 2006
STATUS
approved