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Expansion of (1+x^2)/(1+x+x^4) mod 3.
1

%I #11 Apr 27 2017 10:17:13

%S 1,2,2,1,1,0,1,1,1,2,0,2,0,1,2,2,1,1,0,1,1,1,2,0,2,0,1,2,2,1,1,0,1,1,

%T 1,2,0,2,0,1,2,2,1,1,0,1,1,1,2,0,2,0,1,2,2,1,1,0,1,1,1,2,0,2,0,1,2,2,

%U 1,1,0,1,1,1,2,0,2,0

%N Expansion of (1+x^2)/(1+x+x^4) mod 3.

%C Periodic with period (1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 2, 0).

%D Arthur Gill, Linear Sequential Circuits, McGraw-Hill, 1966, Eq. (17-11).

%H Colin Barker, <a href="/A285194/b285194.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).

%F From _Colin Barker_, Apr 27 2017: (Start)

%F G.f.: (2*x^11 + 2*x^9 + x^8 + x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2*x + 1)/(1 - x^13).

%F a(n) = a(n-13) for n>12.

%F (End)

%p t5:=(1+x^2)/(1+x+x^4);

%p t6:=series(%,x,120):

%p t7:=seriestolist(%);

%p t8:=% mod 3;

%o (PARI) Vec((2*x^11 + 2*x^9 + x^8 + x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2*x + 1)/(1 - x^13) + O(x^100)) \\ _Colin Barker_, Apr 27 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Apr 26 2017