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%I #22 Sep 08 2022 08:44:44
%S 1,3,6,9,19,30,63,99,208,327,687,1080,2269,3567,7494,11781,24751,
%T 38910,81747,128511,269992,424443,891723,1401840,2945161,4629963,
%U 9727206,15291729,32126779,50505150,106107543,166807179,350449408,550926687,1157455767,1819587240
%N a(n+2) = 3*a(n) - a(n-2) with a(0) = 1, a(1) = 3, a(2) = 6.
%H Vincenzo Librandi, <a href="/A018186/b018186.txt">Table of n, a(n) for n = 0..1000</a>
%H J. L. Simons, <a href="http://www.rug.nl/staff/j.l.simons/english_)text_diss.pdf">Conditional recurring sequences</a>, Doctor's Thesis, Delft University of Technology, Delft, 1976 (MR 54 #7361).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,1).
%F G.f.: (1+3*x+3*x^2)/(1-3*x^2-x^4).
%t CoefficientList[Series[(1 + 3 x + 3 x^2) / (1 - 3 x^2 - x^4), {x, 0, 40}],x] (* _Vincenzo Librandi_, Sep 10 2013 *)
%t LinearRecurrence[{0,3,0,1},{1,3,6,9},40] (* _Harvey P. Dale_, Jul 19 2015 *)
%o (PARI) lista(nn) = {x = xx + xx*O(xx^nn); expr = (1 + 3*x + 3*x^2)/(1 - 3*x^2 - x^4); for (i = 0, nn, print1(polcoeff(expr, i, xx), ", "););} \\ _Michel Marcus_, Sep 09 2013
%o (PARI) Vec( (1+3*x+3*x^2)/(1-3*x^2-x^4)+O(x^66) ) \\ _Joerg Arndt_, Sep 09 2013
%o (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1+3*x+3*x^2)/(1-3*x^2-x^4)); // _Vincenzo Librandi_, Sep 10 2013
%K nonn,easy
%O 0,2
%A H. J. J. te Riele (Herman.te.Riele(AT)cwi.nl)
%E More terms from _Michel Marcus_, Sep 09 2013
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