This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085281 #25 Nov 12 2024 08:57:30
%S A085281 1,2,5,13,35,97,275,793,2315,6817,20195,60073,179195,535537,1602515,
%T A085281 4799353,14381675,43112257,129271235,387682633,1162785755,3487832977,
%U A085281 10462450355,31385253913,94151567435,282446313697,847322163875,2541932937193,7625731702715,22877060890417,68630914235795,205892205836473
%N A085281 Expansion of (1 - 3*x + x^2)/((1-2*x)*(1-3*x)).
%C A085281 Binomial transform of A005578.
%C A085281 Binomial transform is A085282.
%H A085281 Vincenzo Librandi, <a href="/A085281/b085281.txt">Table of n, a(n) for n = 0..500</a>
%H A085281 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6).
%F A085281 a(n) = 3^(n-1) + 2^(n-1) + 0^n/6.
%F A085281 a(n) = A007689(n-1), n > 0. - _R. J. Mathar_, Sep 12 2008
%F A085281 E.g.f.: (1/6)*(1 + 3*exp(2*x) + 2*exp(3*x)). - _G. C. Greubel_, Nov 11 2024
%t A085281 a[n_]:=3^n/3 + 2^n/2; Flatten[Join[{1, Array[a, 50]}]] (* or *)
%t A085281 CoefficientList[Series[(1 - 3*x + x^2)/((1-2*x)*(1-3*x)), {x, 0, 50}], x] (* _Stefano Spezia_, Sep 09 2018 *)
%t A085281 LinearRecurrence[{5,-6},{1,2,5},40] (* _Harvey P. Dale_, Jun 14 2022 *)
%o A085281 (Magma) [3^n/3+2^n/2+0^n/6: n in [0..40]]; // _Vincenzo Librandi_, May 29 2011
%o A085281 (SageMath)
%o A085281 def A085281(n): return 2^(n-1) +3^(n-1) +int(n==0)/6
%o A085281 [A085281(n) for n in range(41)] # _G. C. Greubel_, Nov 11 2024
%Y A085281 Cf. A005578, A007689, A085282.
%K A085281 easy,nonn
%O A085281 0,2
%A A085281 _Paul Barry_, Jun 25 2003