 | ECS #425 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Sequence} \left( {\rm Union} \left( Z,{\rm Prod}
\left( Z,Z,Z,Z,Z,{\rm Sequence} \left( Z \right) \right) \right)
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -f \left( n+3 \right) +2\,f \left( n+4
\right) -f \left( n+5 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =1,f \left( 2 \right) =1,f \left( 3 \right) =1,f \left( 4
\right) =1 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+2\,{\rm \_Z}-{{\rm \_Z}}^{2}+{{
\rm \_Z}}^{5} \right) }{\frac {1}{3017}}\, \left( 490\,\alpha+135\,{
\alpha}^{4}+225\,{\alpha}^{3}+375\,{\alpha}^{2}+81 \right) {\alpha}^{-1
-n}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+x}{-1+2\,x-{x}^{2}+{x}^{5}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).