A144689 A098777 mod 7.

1, 6, 5, 2, 2, 2, 2, 4, 1, 6, 6, 6, 6, 5, 3, 4, 4, 4, 4, 1, 2, 5, 5, 5, 5, 3, 6, 1, 1, 1, 1, 2, 4, 3, 3, 3, 3, 6, 5, 2, 2, 2, 2, 4, 1, 6, 6, 6, 6, 5, 3, 4, 4, 4, 4, 1, 2, 5, 5, 5, 5, 3, 6, 1, 1, 1, 1, 2, 4, 3, 3, 3, 3, 6, 5, 2, 2, 2, 2, 4, 1, 6, 6, 6, 6, 5, 3, 4, 4, 4, 4, 1, 2, 5, 5, 5, 5, 3, 6, 1, 1

Offset: 0

Author

N. J. A. Sloane, Feb 08 2009

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• R. Bacher and P. Flajolet, Pseudo-factorials, Elliptic Functions and Continued Fractions, arXiv:0901.1379 [math.CA], 2009.

Programs

Maple

a:= proc(n) option remember; `if`(n=0,1,(-1)^n*add(binomial(n-1,k)*a(k)*a(n-1-k),k=0..n-1)) end: seq(modp(a(n),7), n=0..100); # Muniru A Asiru, Jul 29 2018

Mathematica

b[0] = 1; b[n_] := b[n] = (-1)^n Sum[Binomial[n-1, k] b[k] b[n-k-1], {k, 0, n-1}];
a[n_] := Mod[b[n], 7]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 29 2018 *)

Formula

For n >= 0 has period 36.

From Chai Wah Wu, Jun 09 2016: (Start)

a(n) = a(n-1) - a(n-18) + a(n-19) for n > 19.

G.f.: (1 + 5*x - x^2 - 3*x^3 + 2*x^7 - 3*x^8 + 5*x^9 - x^13 - 2*x^14 + x^15 + x^18 + 2*x^19)/(1 - x + x^18 - x^19). (End)