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A036543 a(n) = T(3,n), array T given by A048471.

%I A036543 #28 Sep 08 2022 08:44:52
%S A036543 1,9,33,105,321,969,2913,8745,26241,78729,236193,708585,2125761,
%T A036543 6377289,19131873,57395625,172186881,516560649,1549681953,4649045865,
%U A036543 13947137601,41841412809,125524238433,376572715305,1129718145921
%N A036543 a(n) = T(3,n), array T given by A048471.
%H A036543 Vincenzo Librandi, <a href="/A036543/b036543.txt">Table of n, a(n) for n = 0..1000</a>
%H A036543 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A036543 Binomial transform of A084242. Second binomial transform of periodic sequence A010688. - _Paul Barry_, May 23 2003
%F A036543 From _Paul Barry_, May 23 2003: (Start)
%F A036543 a(n) = 4*3^n - 3;
%F A036543 G.f.: (1+5*x)/((1-x)*(1-3*x));
%F A036543 E.g.f.: 4*exp(3*x) - 3*exp(x). (End)
%F A036543 a(n) = 4*a(n-1) - 3*a(n-2); a(0)=1, a(1)=9. - _Harvey P. Dale_, Aug 16 2011
%F A036543 a(n) = 3*a(n-1) + 6. - _Vincenzo Librandi_, Nov 11 2011
%F A036543 a(n) = A171498(n) - 2. - _Philippe Deléham_, Apr 13 2013
%t A036543 4*3^Range[0,25]-3 (* or *) LinearRecurrence[{4,-3},{1,9},25] (* _Harvey P. Dale_, Aug 16 2011 *)
%o A036543 (Magma) [4*3^n-3: n in [0..30]]; // _Vincenzo Librandi_, Nov 11 2011
%o A036543 (PARI) vector(30, n, n--; 4*3^n-3) \\ _G. C. Greubel_, Nov 23 2018
%o A036543 (Sage) [4*3^n-3 for n in range(30)] # _G. C. Greubel_, Nov 23 2018
%Y A036543 n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+2) for n=1, 2, 3, ...
%Y A036543 Cf. A146541 (inv. bin. transf.)
%K A036543 nonn,easy
%O A036543 0,2
%A A036543 _Clark Kimberling_