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A159987
Catalan numbers read modulo 8.
2
1, 1, 2, 5, 6, 2, 4, 5, 6, 6, 4, 2, 4, 4, 0, 5, 6, 6, 4, 6, 4, 4, 0, 2, 4, 4, 0, 4, 0, 0, 0, 5, 6, 6, 4, 6, 4, 4, 0, 6, 4, 4, 0, 4, 0, 0, 0, 2, 4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 6, 6, 4, 6, 4, 4, 0, 6, 4, 4, 0, 4, 0, 0, 0, 6, 4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 4, 0, 0, 0, 4, 0
OFFSET
0,3
LINKS
Rob Burns, Asymptotic density of Catalan numbers modulo 3 and powers of 2, arXiv:1611.03705 [math.NT], 2016.
Shu-Chung Liu and Jean C.-C. Yeh, Catalan numbers modulo 2^k, J. Int. Seq., Vol. 13 (2010), Article 10.5.4.
FORMULA
a(n) = A000108(n) mod 8.
a(n) == A159981(n) (mod 4). - R. J. Mathar, Apr 30 2009
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:
A159987 := proc(n) A000108(n) mod 8 ; end:
seq(A159987(n), n=0..120) ; # R. J. Mathar, Apr 30 2009
MATHEMATICA
Table[Mod[CatalanNumber[n], 8], {n, 0, 100}] (* Amiram Eldar, Jan 26 2021 *)
CROSSREFS
Sequence in context: A318388 A145058 A103130 * A143678 A346042 A021800
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 28 2009
STATUS
approved