A133886 a(n) = binomial(n+6,n) mod 6.

1, 1, 4, 0, 0, 0, 0, 0, 3, 1, 4, 4, 0, 0, 0, 0, 3, 3, 4, 4, 4, 0, 0, 0, 3, 3, 0, 4, 4, 4, 0, 0, 3, 3, 0, 0, 4, 4, 4, 0, 3, 3, 0, 0, 0, 4, 4, 4, 3, 3, 0, 0, 0, 0, 4, 4, 1, 3, 0, 0, 0, 0, 0, 4, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 4, 0, 0, 0, 0, 0, 3, 1, 4, 4, 0, 0, 0, 0, 3, 3, 4, 4, 4, 0, 0, 0, 3, 3, 0, 4, 4, 4, 0, 0, 3

Offset: 0

Author

Hieronymus Fischer, Oct 10 2007

Keywords

• nonn
• easy

Comments

Periodic with length 2*6^2 = 72.

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 1).

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133876, A133880, A133890, A133900, A133910.

Programs

Maple

A133886:=n->binomial(n+6,6) mod 6; seq(A133886(n), n=0..100); # Wesley Ivan Hurt, Apr 30 2014

Mathematica

Table[Mod[Binomial[n+6,n],6],{n,0,110}] (* Harvey P. Dale, May 04 2013 *)

Formula

a(n) = binomial(n+6,6) mod 6.

G.f.: g(x) = (1+x+4*x^2-6*x^9-6*x^56+4*x^63+x^64+x^65+3*x^8*(1+x)(1-x^56)/(1-x^8)+4*x^9(1+x+x^2)(1-x^54)/(1-x^9))/(1-x^72).

a(n) = a(n-1)-a(n-2)+a(n-8)+a(n-11)-a(n-17)-a(n-20)-a(n-24)+a(n-25)+a(n-29)+ a(n-32)- a(n-38)-a(n-41)+a(n-47)-a(n-48)+a(n-49). - Harvey P. Dale, May 04 2013