A136302 - OEIS

%I #25 Apr 19 2021 08:15:43

%S 2,6,15,35,81,188,437,1016,2362,5491,12765,29675,68986,160373,372822,

%T 866706,2014847,4683951,10888865,25313540,58846841,136802308,

%U 318026782,739322571,1718716457,3995531011,9288482690,21593102505,50197873146,116695897118,271285047567

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

%H G. C. Greubel, <a href="/A136302/b136302.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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1).

%F G.f.: z*(2 + z^2)/(1 - 3*z + 2*z^2 - z^3).

%F a(n+3) = 3*a(n+2) - 2*a(n+1) + a(n) (n>=0). - _Richard Choulet_, Apr 07 2009

%F a(n) = 2*A095263(n) + A095263(n-2). - _R. J. Mathar_, Feb 29 2016

%p a:= n-> (<<6|2|1>>. <<3|1|0>, <-2|0|1>, <1|0|0>>^n)[1, 3]:

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Aug 14 2008

%t LinearRecurrence[{3,-2,1}, {2,6,15}, 41] (* _G. C. Greubel_, Apr 12 2021 *)

%o (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 (Sage)

%o def A136302_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( x*(2+x^2)/(1-3*x+2*x^2-x^3) ).list()

%o a=A136302_list(41); a[1:] # _G. C. Greubel_, Apr 12 2021

%Y Cf. A095263, A136303, A136304, A136305.

%K nonn,easy

%O 1,1

%A _Richard Choulet_, Mar 22 2008

%E More terms from _Alois P. Heinz_, Aug 14 2008