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A188146 Three interleaved 1st-order polynomials: a(3*n) = 1+4*n, a(1+3*n) = 3+4*n, a(2+3*n) = 1+n.

%I A188146 #20 Feb 02 2021 20:51:07
%S A188146 1,3,1,5,7,2,9,11,3,13,15,4,17,19,5,21,23,6,25,27,7,29,31,8,33,35,9,
%T A188146 37,39,10,41,43,11,45,47,12,49,51,13,53,55,14,57,59,15,61,63,16,65,67,
%U A188146 17,69,71,18,73,75,19,77,79,20,81,83,21,85,87,22,89,91,23,93,95,24,97,99,25,101,103,26,105,107,27,109,111
%N A188146 Three interleaved 1st-order polynomials: a(3*n) = 1+4*n, a(1+3*n) = 3+4*n, a(2+3*n) = 1+n.
%H A188146 Colin Barker, <a href="/A188146/b188146.txt">Table of n, a(n) for n = 0..1000</a>
%H A188146 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A188146 a(n)= 2*a(n-3) - a(n-6).
%F A188146 a(3*n) + a(1+3*n) + a(2+3*n) = 5+9*n.
%F A188146 a(n) = n + 1 - (-1)^n*A099254(n-1). - _R. J. Mathar_, Mar 31 2011
%F A188146 G.f.: ( 1+3*x+x^2+3*x^3+x^4 ) / ( (x-1)^2*(1+x+x^2)^2 ). - _R. J. Mathar_, Mar 31 2011
%F A188146 a(n) = (9*(n+1) + sqrt(3)*(3*n+4)*sin((2*Pi*n)/3) + 3*n*cos((2*Pi*n)/3)) / 9. - _Colin Barker_, Mar 06 2017
%t A188146 CoefficientList[Series[(1+3x+x^2+3x^3+x^4)/((x-1)^2(1+x+x^2)^2), {x,0,85}],x] (* _Harvey P. Dale_, Apr 09 2011 *)
%o A188146 (PARI) Vec((1+3*x+x^2+3*x^3+x^4 ) / ((x-1)^2*(1+x+x^2)^2) + O(x^100)) \\ _Colin Barker_, Mar 06 2017
%K A188146 nonn,less,easy
%O A188146 0,2
%A A188146 _Paul Curtz_, Mar 22 2011