 | ECS #940: Arithmetic sequence |
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1. Description
4 n + 3
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Union} \left( {\rm Prod} \left( {\rm Union} \left( Z,Z,
Z,Z \right) ,{\rm Sequence} \left( Z \right) ,{\rm Sequence} \left( Z
\right) \right) ,{\rm Prod} \left( {\rm Union} \left( Z,Z,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) -4\,n-3=0,f \left( 0 \right) =0,f \left( 1
\right) =7,f \left( 2 \right) =11 \right\}
other formats
3.3. Closed form
\displaystyle
3+4\,n+\cases{-3&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {x \left( -7+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).