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