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

0,3

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).

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

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 *)

Crossrefs

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

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

Sequence in context: A280492 A089371 A318679 * A378650 A378653 A061859

Adjacent sequences: A133883 A133884 A133885 * A133887 A133888 A133889

Keyword

nonn,easy

Author

Hieronymus Fischer, Oct 10 2007

Status

approved