A639. Multi-partitions
Louis Rogliano
Désignons parf ib(n)lenieme nombre de Fibonacci puis construisons l’ensembleEn tel que : En={f ib(2), . . . , f ib(2n),
i=2n∑
i=2
f ib(i)−2f ib(2n)}. Cet ensemble répond à la question.
Exemple :
E7 ={1,2,3,5,8,13,21,34,55,89,144,233,377,231}pour un total de1216.
Les partitions sont :
{1,2,3,5,8,13,21,34,55,89,144,233} {377,231} 608 608 {1,2,3,5,8,13,21,34,55,89,377} {231,144,233} 608 608 {1,2,3,5,8,13,21,34,377,144} {231,233,55,89} 608 608 {1,2,3,5,8,13,377,144,55} {231,233,89,21,34} 608 608 {1,2,3,5,377,144,55,21} {231,233,89,34,8,13} 608 608 {1,2,377,144,55,21,8} {231,233,89,34,13,3,5} 608 608
En adaptant cette solution à l’exemple numérique nous obtenons l’ensemble de16éléments suivant :
E8 ={1,2,3,5,8,13,21,34,55,89,144,233,377,1646,2021,610}pour un total de5262.
Les partitions sont :
{1,2,3,5,8,13,21,34,55,89,144,233,377,1646} {2021,610} 2631 2631 {1,2,3,5,8,13,21,34,55,89,144,1646,610} {2021,233,377} 2631 2631 {1,2,3,5,8,13,21,34,55,1646,610,233} {2021,377,89,144} 2631 2631 {1,2,3,5,8,13,21,1646,610,233,89} {2021,377,144,34,55} 2631 2631 {1,2,3,5,8,1646,610,233,89,34} {2021,377,144,55,13,21} 2631 2631 {1,2,3,1646,610,233,89,34,13} {2021,377,144,55,21,5,8} 2631 2631 {1,1646,610,233,89,34,13,5} {2021,377,144,55,21,8,2,3} 2631 2631
1
