cp's OEIS Frontend

A144689 A098777 mod 7.

%I A144689 #14 Jul 29 2018 08:09:35
%S A144689 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,
%T A144689 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,
%U A144689 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
%N A144689 A098777 mod 7.
%H A144689 Muniru A Asiru, <a href="/A144689/b144689.txt">Table of n, a(n) for n = 0..1000</a>
%H A144689 R. Bacher and P. Flajolet, <a href="https://arxiv.org/abs/0901.1379">Pseudo-factorials, Elliptic Functions and Continued Fractions</a>, arXiv:0901.1379 [math.CA], 2009.
%F A144689 For n >= 0 has period 36.
%F A144689 From _Chai Wah Wu_, Jun 09 2016: (Start)
%F A144689 a(n) = a(n-1) - a(n-18) + a(n-19) for n > 19.
%F A144689 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)
%p A144689 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
%t A144689 b[0] = 1; b[n_] := b[n] = (-1)^n Sum[Binomial[n-1, k] b[k] b[n-k-1], {k, 0, n-1}];
%t A144689 a[n_] := Mod[b[n], 7]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jul 29 2018 *)
%K A144689 nonn
%O A144689 0,2
%A A144689 _N. J. A. Sloane_, Feb 08 2009