 | ECS #384 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Union} \left( C,Z \right) ,C={\rm Prod} \left( B,Z
\right) ,E={\rm Union} \left( S,B \right) ,S={\rm Prod} \left( C,E
\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+2
\right) -1=0,f \left( 0 \right) =0,f \left( 1 \right) =0,f \left( 2
\right) =0,f \left( 3 \right) =1 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-2\,{\rm \_Z}+{{\rm \_Z}}^{3}
\right) }-1/5\, \left( -8+6\,{\alpha}^{2}+7\,\alpha \right) {\alpha}^{
-1-n}+\cases{1&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {{x}^{3}}{1-2\,x+{x}^{3}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).