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.

A074610 a(n) = 3^n + 9^n.

This page as a plain text file.
%I A074610 #21 Jan 14 2024 02:30:08
%S A074610 2,12,90,756,6642,59292,532170,4785156,43053282,387440172,3486843450,
%T A074610 31381236756,282430067922,2541867422652,22876797237930,
%U A074610 205891146443556,1853020231898562,16677181828806732,150094635684419610
%N A074610 a(n) = 3^n + 9^n.
%H A074610 G. C. Greubel, <a href="/A074610/b074610.txt">Table of n, a(n) for n = 0..1000</a>
%H A074610 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-27).
%F A074610 From _Mohammad K. Azarian_, Jan 11 2009: (Start)
%F A074610 G.f.: 1/(1-3*x) + 1/(1-9*x).
%F A074610 E.g.f.: exp(3*x) + exp(9*x). (End)
%F A074610 a(n) = 12*a(n-1) - 27*a(n-2) with a(0)=2, a(1)=12. - _Vincenzo Librandi_, Jul 21 2010
%F A074610 a(n) = 2*A025551(n). - _G. C. Greubel_, Jan 13 2024
%t A074610 Table[3^n + 9^n, {n, 0, 25}]
%t A074610 LinearRecurrence[{12,-27},{2,12},20] (* _Harvey P. Dale_, May 18 2023 *)
%o A074610 (Magma) [3^n+9^n: n in [0..30]]; // _G. C. Greubel_, Jan 13 2024
%o A074610 (SageMath) [3^n+9^n for n in range(31)] # _G. C. Greubel_, Jan 13 2024
%Y A074610 Cf. A000051, A007689, A025551, A034472, A034474, A034491, A052539.
%Y A074610 Cf. A062394, A062395, A062396, A063376, A063481, A074600..A074624.
%K A074610 easy,nonn
%O A074610 0,1
%A A074610 _Robert G. Wilson v_, Aug 25 2002