 | ECS #680: A simple context-free grammar in a labelled universe |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Prod} \left( Z,C \right) ,C={\rm Union} \left( B,S,Z
\right) ,S={\rm Prod} \left( B,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 4\,{n}^{5}-48+38\,{n}^{4}+120\,{n}^{3}-4\,n+130\,{n}^{
2} \right) f \left( n \right) + \left( -5\,{n}^{4}-168-52\,{n}^{3}-193
\,{n}^{2}-302\,n \right) f \left( n+1 \right) + \left( 96+3\,{n}^{3}+92
\,n+29\,{n}^{2} \right) f \left( 2+n \right) + \left( -52-3\,{n}^{2}-25
\,n \right) f \left( n+3 \right) + \left( 6+n \right) f \left( n+4
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =0,f \left( 2
\right) =0,f \left( 3 \right) =0,f \left( 4 \right) =24,f \left( 5
\right) =240 \right\}
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3.3. Asymptotics
4. Exponential generating function
\displaystyle
-1/2\,{\frac {-1+x+\sqrt {1-2\,x+{x}^{2}-4\,{x}^{3}}}{{x}^{2}}}+1/2\,{
\frac {-1+x+\sqrt {1-2\,x+{x}^{2}-4\,{x}^{3}}}{x}}-x
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).