 | ECS #1063: A simple regular expression |
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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 Prod} \left( {\rm Union} \left( {
\rm Prod} \left( Z,Z \right) ,{\rm Sequence} \left( Z \right) \right)
,Z,Z \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -f \left( n+1 \right) -f \left( n+3
\right) -f \left( n+4 \right) +f \left( n+5 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =0,f \left( 2 \right) =1,f \left( 3
\right) =1,f \left( 4 \right) =3 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-{\rm \_Z}-{{\rm \_Z}}^{4}+{{\rm \_Z
}}^{5}-{{\rm \_Z}}^{2} \right) }-{\frac {1}{8519}}\, \left( -389-2111\,
\alpha+619\,{\alpha}^{2}-358\,{\alpha}^{3}+541\,{\alpha}^{4} \right) {
\alpha}^{-1-n}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {-1+x}{1-x-{x}^{4}+{x}^{5}-{x}^{2}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).