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A137229 Expansion of g.f. x/((1-x)*(1-3*x+2*x^2-x^3)).

%I A137229 #31 Apr 19 2021 08:53:06
%S A137229 1,4,11,27,64,150,350,815,1896,4409,10251,23832,55404,128800,299425,
%T A137229 696080,1618191,3761839,8745216,20330162,47261894,109870575,255418100,
%U A137229 593775045,1380359511,3208946544,7459895656,17342153392,40315615409,93722435100,217878227875
%N A137229 Expansion of g.f. x/((1-x)*(1-3*x+2*x^2-x^3)).
%C A137229 Previous name was: Transform of A000217 without the initial 0 by the T_{0,0} transformation (see link).
%C A137229 Partial sums of A095263. - _R. J. Mathar_, Nov 04 2008
%H A137229 G. C. Greubel, <a href="/A137229/b137229.txt">Table of n, a(n) for n = 1..1000</a>
%H A137229 Richard Choulet, <a href="https://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A137229 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,3,-1).
%F A137229 O.g.f: x/((1-x)*(1 -3*x +2*x^2 -x^3)).
%F A137229 a(n) = term (4,1) in the 4x4 matrix [3,1,0,0; -2,0,1,0; 1,0,0,0; 1,0,0,1]^(n). - _Alois P. Heinz_, Jul 24 2008
%p A137229 a:= n-> (<<3|1|0|0>, <-2|0|1|0>, <1|0|0|0>, <1|0|0|1>>^n)[4, 1]:
%p A137229 seq(a(n), n=1..50);  # _Alois P. Heinz_, Jul 24 2008
%t A137229 LinearRecurrence[{4,-5,3,-1},{1,4,11,27},40] (* _Harvey P. Dale_, Nov 10 2014 *)
%o A137229 (Magma) I:=[1,4,11,27]; [n le 4 select I[n] else 4*Self(n-1) -5*Self(n-2) +3*Self(n-3) -Self(n-4): n in [1..40]]; // _G. C. Greubel_, Apr 17 2021
%o A137229 (Sage)
%o A137229 def A137229_list(prec):
%o A137229     P.<x> = PowerSeriesRing(ZZ, prec)
%o A137229     return P( x/((1-x)*(1-3*x+2*x^2-x^3)) ).list()
%o A137229 a=A137229_list(41); a[1:] # _G. C. Greubel_, Apr 17 2021
%Y A137229 Cf. A136302, A136303, A136304, A136305.
%K A137229 easy,nonn
%O A137229 1,2
%A A137229 _Richard Choulet_, Apr 05 2008
%E A137229 New name using g.f., _Joerg Arndt_, Apr 18 2021