 | ECS #68: Integer composition |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
integer composition of size n: Sequences (n1,...,nk) such that n1+n2+...+nk=n, with ni and k positive integers
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Sequence} \left( {\rm Sequence} \left( a,1\leq {\rm
card} \right) \right) ,a={\rm Atom} \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 2\,f \left( n \right) -f \left( n+1 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
{2}^{n-1}+\cases{1/2&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+x}{-1+2\,x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).