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

Author

Philippe Deléham, Apr 28 2009

Keywords

• easy
• nonn

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.

Crossrefs

Cf. A000108, A159981.

Programs

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 *)

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