Geodesic
An identity generator: basic commutators
The electronic journal of combinatorics, Tome 15 (2008)
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We introduce a group theoretical tool on which one can derive a family of identities from sequences that are defined by a recursive relation. As an illustration it is shown that $$\sum_{i=1}^{n-1}F_{n-i}F_i^2 ={1\over2}\sum_{i=1}^n(-1)^{n-i}(F_{2i}-F_i) ={F_{n+1}\choose2}-{F_n\choose2}, $$ where $\{F_n\}$ denotes the sequence of Fibonacci numbers.
DOI : 10.37236/890
Classification : 05A19, 68R15, 11B39, 20E05
Mots-clés : group theoretical tool, family of identities, sequences, recursive relation, Fibonacci numbers 
@article{10_37236_890,
     author = {M. Farrokhi D. G.},
     title = {An identity generator: basic commutators},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/890},
     zbl = {1160.05308},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/890/}
}
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M. Farrokhi D. G. An identity generator: basic commutators. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/890

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