A159987 Catalan numbers read modulo 8.

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

Table of n, a(n) for n=0..104.

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

Cf. A000108, A159981.

Sequence in context: A318388 A145058 A103130 * A143678 A346042 A021800

Adjacent sequences: A159984 A159985 A159986 * A159988 A159989 A159990

Keyword

easy,nonn

Author

Philippe Deléham, Apr 28 2009

Status

approved