 | ECS #203: Denumerant |
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1. Description
number of ways to make n cents with coins of 1 1 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( Z \right) ,{\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\{ 6\,f \left( n \right) +6\,f \left( n+1 \right) -{n}^{3}-9\,{n}
^{2}-26\,n-24=0,f \left( 0 \right) =1 \right\}
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3.3. Closed form
\displaystyle
{\frac {15}{16}}+{\frac {17}{12}}\,n+5/8\,{n}^{2}+1/12\,{n}^{3}+1/16\,
\left( -1 \right) ^{-n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {1}{ \left( -1+x \right) ^{3} \left( -1+{x}^{2} \right) }}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).