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A136302 Transform of A000027 by the T_{1,1} transformation (see link).

%I A136302 #25 Apr 19 2021 08:15:43
%S A136302 2,6,15,35,81,188,437,1016,2362,5491,12765,29675,68986,160373,372822,
%T A136302 866706,2014847,4683951,10888865,25313540,58846841,136802308,
%U A136302 318026782,739322571,1718716457,3995531011,9288482690,21593102505,50197873146,116695897118,271285047567
%N A136302 Transform of A000027 by the T_{1,1} transformation (see link).
%H A136302 G. C. Greubel, <a href="/A136302/b136302.txt">Table of n, a(n) for n = 1..1000</a>
%H A136302 Richard Choulet, <a href="https://www.apmep.fr/IMG/pdf/curtz1.pdf">Curtz-like transformation</a>.
%H A136302 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).
%F A136302 G.f.: z*(2 + z^2)/(1 - 3*z + 2*z^2 - z^3).
%F A136302 a(n+3) = 3*a(n+2) - 2*a(n+1) + a(n) (n>=0). - _Richard Choulet_, Apr 07 2009
%F A136302 a(n) = 2*A095263(n) + A095263(n-2). - _R. J. Mathar_, Feb 29 2016
%p A136302 a:= n-> (<<6|2|1>>. <<3|1|0>, <-2|0|1>, <1|0|0>>^n)[1, 3]:
%p A136302 seq(a(n), n=1..40);  # _Alois P. Heinz_, Aug 14 2008
%t A136302 LinearRecurrence[{3,-2,1}, {2,6,15}, 41] (* _G. C. Greubel_, Apr 12 2021 *)
%o A136302 (Magma) I:=[2,6,15]; [n le 3 select I[n] else 3*Self(n-1) -2*Self(n-2) +Self(n-3): n in [1..41]]; // _G. C. Greubel_, Apr 12 2021
%o A136302 (Sage)
%o A136302 def A136302_list(prec):
%o A136302     P.<x> = PowerSeriesRing(ZZ, prec)
%o A136302     return P( x*(2+x^2)/(1-3*x+2*x^2-x^3) ).list()
%o A136302 a=A136302_list(41); a[1:] # _G. C. Greubel_, Apr 12 2021
%Y A136302 Cf. A095263, A136303, A136304, A136305.
%K A136302 nonn,easy
%O A136302 1,1
%A A136302 _Richard Choulet_, Mar 22 2008
%E A136302 More terms from _Alois P. Heinz_, Aug 14 2008