 | ECS #935: Arithmetic sequence |
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1. Description
2 n + 1
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Union} \left( {\rm Prod} \left( {\rm Union} \left( Z,Z
\right) ,{\rm Sequence} \left( Z \right) ,{\rm Sequence} \left( Z
\right) \right) ,{\rm Prod} \left( {\rm Union} \left( Z \right) ,{
\rm Sequence} \left( Z \right) \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) -2\,n-1=0,f \left( 0 \right) =0,f \left( 1
\right) =3,f \left( 2 \right) =5 \right\}
other formats
3.3. Closed form
\displaystyle
1+2\,n+\cases{-1&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {x \left( -3+x \right) }{ \left( -1+x \right) ^{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).