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

0,2

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.

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)

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 *)

Crossrefs

Sequence in context: A374529 A112282 A098866 * A221215 A199180 A197265

Adjacent sequences: A144686 A144687 A144688 * A144690 A144691 A144692

Keyword

nonn

Author

N. J. A. Sloane, Feb 08 2009

Status

approved