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%I #27 Apr 26 2023 19:21:04
%S 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,
%T 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,
%U 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
%N a(n) = binomial(n+6,n) mod 6.
%C Periodic with length 2*6^2 = 72.
%H Ray Chandler, <a href="/A133886/b133886.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, 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).
%F a(n) = binomial(n+6,6) mod 6.
%F 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).
%F 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
%p A133886:=n->binomial(n+6,6) mod 6; seq(A133886(n), n=0..100); # _Wesley Ivan Hurt_, Apr 30 2014
%t Table[Mod[Binomial[n+6,n],6],{n,0,110}] (* _Harvey P. Dale_, May 04 2013 *)
%Y Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.
%Y Cf. A133876, A133880, A133890, A133900, A133910.
%K nonn,easy
%O 0,3
%A _Hieronymus Fischer_, Oct 10 2007
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