 | ECS #380: Fibonacci like recurrence |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Sequence} \left( {\rm Prod} \left( Z,{\rm Sequence}
\left( {\rm Prod} \left( Z,Z,Z,Z,Z,Z,Z \right) \right) \right)
\right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) +f \left( n+6 \right) -f \left( n+7
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2
\right) =1,f \left( 3 \right) =1,f \left( 4 \right) =1,f \left( 5
\right) =1,f \left( 6 \right) =1,f \left( 7 \right) =1 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{7}+{\rm \_Z} \right)
}{\frac {1}{870199}}\, \left( -7776\,\alpha+63504\,{\alpha}^{6}+74088\,
{\alpha}^{5}+86436\,{\alpha}^{4}+100842\,{\alpha}^{3}+117649\,{\alpha}^
{2}+54432 \right) {\alpha}^{-1-n}+\cases{1&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+{x}^{7}}{-1+{x}^{7}+x}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).