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A135263 a(n) = 2*A132357(n).

%I A135263 #21 Sep 08 2022 08:45:32
%S A135263 2,8,28,82,244,728,2186,6560,19684,59050,177148,531440,1594322,
%T A135263 4782968,14348908,43046722,129140164,387420488,1162261466,3486784400,
%U A135263 10460353204,31381059610,94143178828,282429536480,847288609442
%N A135263 a(n) = 2*A132357(n).
%C A135263 Digital roots yield a hexaperiodic sequence A010888(a(n))= 2, (8, 1, 1, 1, 8, 8,...), the period of length 6 put in parenthesis. Digital roots of A132357 are also hexaperiodic: 1, (4, 5, 5, 5, 4, 4, ....).
%H A135263 G. C. Greubel, <a href="/A135263/b135263.txt">Table of n, a(n) for n = 0..1000</a>
%H A135263 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-1,3).
%F A135263 a(n) = 3*a(n-1) - a(n-3) + a(n-4).
%F A135263 G.f.: 2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)). - _Colin Barker_, Jun 16 2012
%p A135263 seq(coeff(series(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 21 2019
%t A135263 LinearRecurrence[{3,0,-1,3}, {2,8,28,82}, 30] (* _G. C. Greubel_, Oct 07 2016 *)
%o A135263 (PARI) my(x='x+O('x^30)); Vec(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2))) \\ _G. C. Greubel_, Nov 21 2019
%o A135263 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2)) )); // _G. C. Greubel_, Nov 21 2019
%o A135263 (Sage)
%o A135263 def A135263_list(prec):
%o A135263     P.<x> = PowerSeriesRing(ZZ, prec)
%o A135263     return P(2*(1+x+2*x^2)/((1+x)*(1-3*x)*(1-x+x^2))).list()
%o A135263 A135263_list(30) # _G. C. Greubel_, Nov 21 2019
%o A135263 (GAP) a:=[2,8,28,82];; for n in [5..30] do a[n]:=3*a[n-1]-a[n-3]+ 3*a[n-4]; od; a; # _G. C. Greubel_, Nov 21 2019
%Y A135263 Cf. A133448 (hexaperiodic sequence of digital roots).
%K A135263 nonn,less,easy
%O A135263 0,1
%A A135263 _Paul Curtz_, Dec 02 2007
%E A135263 Edited and extended by _R. J. Mathar_, Jul 22 2008