ECS #197: Denumerant
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1. Description

number of ways to make n cents with coins of 1 1 2 4 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( {\rm Prod} \left( Z,Z \right) \right) ,{\rm Sequence} \left( {\rm Prod} \left( Z,Z,Z,Z \right) \right) \right) \right\}
other formats

3. Coefficients

3.1. First terms

3.2. Recurrence

\displaystyle \left\{ 6\,f \left( n \right) +12\,f \left( n+1 \right) +12\,f \left( n+2 \right) +12\,f \left( n+3 \right) +6\,f \left( n+4 \right) -{n}^{3} -18\,{n}^{2}-107\,n-210=0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2 \right) =4,f \left( 3 \right) =6 \right\}
other formats

3.3. Closed form

\displaystyle {\frac {7}{8}}+1/4\,{n}^{2}+{\frac {85}{96}}\,n+1/48\,{n}^{3}+1/32\, \left( -1 \right) ^{-n}n+1/8\, \left( -1 \right) ^{-n}+\sum _{\alpha={ \rm RootOf} \left( {{\rm \_Z}}^{2}+1 \right) }-1/16\,{\alpha}^{-n-1}
other formats

3.4. Asymptotics

4. Ordinary generating function

\displaystyle {\frac {1}{ \left( -1+x \right) ^{2} \left( -1+{x}^{2} \right) \left( -1+{x}^{4} \right) }}
other formats

5. References

EIS A008804

6. Random structure


Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).

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Based on commit 9d1e479..., Fri Jul 10 14:52:30 2009 +0200.
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