 | ECS #343: k-gonal numbers |
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1. Description
6-gonal numbers
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Prod} \left( C,C,C \right) ,C={\rm Sequence} \left( Z
\right) ,E={\rm Prod} \left( Z,B \right) ,S={\rm Union} \left( B,E,E,E
,E,E,E \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -2\,f \left( n \right) +7\,{n}^{2}+9\,n+2=0,f \left( 0
\right) =1,f \left( 1 \right) =9 \right\}
other formats
3.3. Closed form
\displaystyle
7/2\,{n}^{2}+9/2\,n+1
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {1+6\,x}{ \left( -1+x \right) ^{3}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).