 | ECS #209: Denumerant |
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1. Description
number of ways to make n cents with coins of 1 2 cents
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( {\rm Sequence} \left( Z \right) ,{\rm
Sequence} \left( {\rm Prod} \left( Z,Z \right) \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) +f \left( n+1 \right) -n-2=0,f \left( 0
\right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
3/4+1/2\,n+1/4\, \left( -1 \right) ^{-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {1}{ \left( -1+x \right) \left( -1+{x}^{2} \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).