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A159981 Catalan numbers read modulo 4. 2
1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Essentially the same as A073267. - R. J. Mathar, May 25 2009
LINKS
Rob Burns, Asymptotic density of Catalan numbers modulo 3 and powers of 2, arXiv:1611.03705 [math.NT], 2016.
Sen-Peng Eu, Shu-Chung Liu and Yeong-Nan Yeh, Catalan and Motzkin numbers modulo 4 and 8, European Journal of Combinatorics, Vol. 29, No. 6 (2008), pp. 1449-1466. [From R. J. Mathar, Apr 30 2009]
Eric Rowland and Reem Yassawi, Profinite automata, Advances in Applied Mathematics, Vol. 85 (2017), pp. 60-83; arXiv preprint, arXiv:1403.7659 [math.DS], 2014-2016. See p. 4, 6 and 7.
FORMULA
a(n) = A000108(n) mod 4.
Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 0 (Burns, 2016). - Amiram Eldar, Jan 26 2021
MAPLE
A000108 := proc(n) binomial(2*n, n)/(n+1) ; end: A159981 := proc(n) A000108(n) mod 4 ; end: seq(A159981(n), n=0..120) ; # R. J. Mathar, Apr 30 2009
MATHEMATICA
Mod[CatalanNumber[Range[0, 110]], 4] (* Harvey P. Dale, Oct 05 2011 *)
PROG
(PARI) A159981(n) = (binomial(2*n, n)/(n+1))%4; \\ Antti Karttunen, Jan 17 2017
CROSSREFS
Sequence in context: A175609 A038717 A073267 * A071858 A122864 A140084
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 28 2009
EXTENSIONS
Extended by R. J. Mathar, Apr 30 2009
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)