OFFSET
0,3
COMMENTS
Essentially the same as A073267. - R. J. Mathar, May 25 2009
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..10000
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
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 28 2009
EXTENSIONS
Extended by R. J. Mathar, Apr 30 2009
STATUS
approved