|
|
A082490
|
|
Exponent of highest power of 3 dividing sum(0<=k<n, C(2n,n)).
|
|
1
|
|
|
0, 1, 2, 0, 2, 3, 1, 2, 4, 0, 1, 2, 0, 3, 4, 2, 3, 5, 1, 2, 3, 1, 3, 4, 2, 3, 6, 0, 1, 2, 0, 2, 3, 1, 2, 4, 0, 1, 2, 0, 4, 5, 3, 4, 6, 2, 3, 4, 2, 4, 5, 3, 4, 7, 1, 2, 3, 1, 3, 4, 2, 3, 5, 1, 2, 3, 1, 4, 5, 3, 4, 6, 2, 3, 4, 2, 4, 5, 3, 4, 8, 0, 1, 2, 0, 2, 3, 1, 2, 4, 0, 1, 2, 0, 3, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
J. Shallit, Number theory and formal languages, in D. A. Hejhal, J. Friedman, M. C. Gutzwiller and A. M. Odlyzko, eds., Emerging Applications of Number Theory, IMA Volumes in Mathematics and Its Applications, V. 109, Springer-Verlag, 1999, pp. 547-570. (Example 1.)
|
|
FORMULA
|
|
|
MAPLE
|
map(t -> padic:-ordp(t, 3), ListTools:-PartialSums([seq(binomial(2*n, n), n=0..100)])); # Robert Israel, Mar 27 2018
|
|
PROG
|
(PARI) s=0; for(n=1, 150, s=s+binomial(2*n-2, n-1); print1(valuation(s, 3)", "))
(PARI) a(n) = valuation(n^2 * binomial(2*n, n), 3); \\ Michel Marcus, Mar 27 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|