Geodesic
Finite sequences dominated by the squares
Journal of integer sequences, Tome 18 (2015) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We evaluate the number $u(n)$ of length-$n$ finite sequences $(a_{k})_{1 \le k \le n}$ of natural numbers that satisfy the inequality $a_{k} \le k^{2}$ for all $k$. We thus determine two recurrence relations for $u(n)$ by two different methods, and we give an explicit expression in closed form for it.
Classification : 05A10, 05A15, 05A19, 11B65, 11B75
Keywords: finite sequence, binomial coefficient, combinatorics, enumeration 
@article{JIS_2015__18_1_a0,
     author = {Haddad, L. and Helou, C.},
     title = {Finite sequences dominated by the squares},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a0/}
}
TY  - JOUR
AU  - Haddad, L.
AU  - Helou, C.
TI  - Finite sequences dominated by the squares
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a0/
LA  - en
ID  - JIS_2015__18_1_a0
ER  - 
%0 Journal Article
%A Haddad, L.
%A Helou, C.
%T Finite sequences dominated by the squares
%J Journal of integer sequences
%D 2015
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a0/
%G en
%F JIS_2015__18_1_a0
Haddad, L.; Helou, C. Finite sequences dominated by the squares. Journal of integer sequences, Tome 18 (2015) no. 1. http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a0/