ECS #1072: 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 Prod} \left( {\rm Sequence} \left( {\rm Union} \left( { \rm Prod} \left( {\rm Sequence} \left( Z \right) ,Z \right) ,Z \right) \right) ,{\rm Union} \left( Z,Z \right) \right) \right\}
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3. Coefficients

3.1. First terms

3.2. Recurrence

\displaystyle \left\{ f \left( n \right) -3\,f \left( n+1 \right) +f \left( n+2 \right) =0,f \left( 0 \right) =0,f \left( 1 \right) =2,f \left( 2 \right) =4 \right\}
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3.3. Closed form

\displaystyle \sum _{\alpha={\rm RootOf} \left( 1-3\,{\rm \_Z}+{{\rm \_Z}}^{2} \right) }2/5\, \left( 4\,\alpha-1 \right) {\alpha}^{-1-n}+ \cases{-2&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics

4. Ordinary generating function

\displaystyle -2\,{\frac {x \left( -1+x \right) }{1-3\,x+{x}^{2}}}
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5. References

EIS A052995

6. Random structure


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

Generated: 2010-02-09 19:01:58 in 1. seconds of elapsed time.
Based on commit 9d1e479..., Fri Jul 10 14:52:30 2009 +0200.
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