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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.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
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
a(n) = A007949(A006134(n)) = A007949 (n^2 * C(2n, n)) (Allouche, Shallit; Zagier) = 2*A007949(n) + A000989(n).
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
Sequence in context: A284592 A071447 A063514 * A328591 A210635 A062242
KEYWORD
nonn,hear
AUTHOR
Ralf Stephan, Apr 28 2003
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)