cp's OEIS Frontend

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.

A083223 a(n) = (5*6^n+(-6)^n)/6.

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%I A083223 #17 Sep 08 2022 08:45:10
%S A083223 1,4,36,144,1296,5184,46656,186624,1679616,6718464,60466176,241864704,
%T A083223 2176782336,8707129344,78364164096,313456656384,2821109907456,
%U A083223 11284439629824,101559956668416,406239826673664,3656158440062976
%N A083223 a(n) = (5*6^n+(-6)^n)/6.
%H A083223 Vincenzo Librandi, <a href="/A083223/b083223.txt">Table of n, a(n) for n = 0..300</a>
%H A083223 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,36).
%F A083223 a(n) = (5*6^n+(-6)^n)/6.
%F A083223 G.f.: (1+4*x)/((1+6*x)*(1-6*x)).
%F A083223 E.g.f.: (5*exp(6*x)+exp(-6*x))/6.
%F A083223 a(n) = 36*a(n-2). - _Wesley Ivan Hurt_, Jun 24 2021
%t A083223 CoefficientList[Series[(1+4x)/((1+6x)(1-6x)),{x,0,50}],x]  (* _Harvey P. Dale_, Mar 01 2011 *)
%o A083223 (Magma) [(5*6^n+(-6)^n)/6: n in [0..25]]; // _Vincenzo Librandi_, Jun 29 2011
%Y A083223 Cf. A083222, A083224.
%K A083223 easy,nonn
%O A083223 0,2
%A A083223 _Paul Barry_, Apr 23 2003