 | ECS #397 |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Set} \left( Z \right) ,C={\rm Set} \left( Z,1\leq {\rm
card} \right) ,S={\rm Prod} \left( C,B,B \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n+2 \right) -5\,f \left( n+1 \right) +6\,f \left( n
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =1 \right\}
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3.3. Closed form
\displaystyle
{3}^{n}-{2}^{n}
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
\left( {{\rm e}^{x}} \right) ^{3}- \left( {{\rm e}^{x}} \right) ^{2}
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It satisfies the following differential equation of order 2:
\displaystyle
\left\{ {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) -5\,{\frac {d}{dx}
}y \left( x \right) +6\,y \left( x \right) =0,y \left( 0 \right) =0,
\mbox {D} \left( y \right) \left( 0 \right) =1 \right\}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).