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 A133647 #22 Jun 02 2025 04:55:59
%S A133647 1,3,12,27,108,243,972,2187,8748,19683,78732,177147,708588,1594323,
%T A133647 6377292,14348907,57395628,129140163,516560652,1162261467,4649045868,
%U A133647 10460353203,41841412812,94143178827,376572715308,847288609443,3389154437772,7625597484987,30502389939948
%N A133647 A133566 * A000244.
%C A133647 A133646 is a companion case.
%H A133647 Harvey P. Dale, <a href="/A133647/b133647.txt">Table of n, a(n) for n = 0..1000</a>
%H A133647 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,9).
%F A133647 A133566 * A000244, where A133566 = an infinite lower triangular matrix and A000244 = [3^0, 3^1, 3^2, ...]. For odd n, a(n) = 3^n. For even n, a(n) = 4 * 3^(n-1).
%F A133647 From _Philippe Deléham_, Apr 06 2012: (Start)
%F A133647 G.f.: (1+3*x+3*x^2)/(1-9*x^2).
%F A133647 a(n+2) = 9*a(n), a(0) = 1, a(1) = 3, a(2) = 12. (End)
%F A133647 From _Amiram Eldar_, Jun 02 2025: (Start)
%F A133647 Sum_{n>=0} 1/a(n) = 47/32.
%F A133647 Sum_{n>=0} (-1)^n/a(n) = 23/32. (End)
%e A133647 a(3) = 27 = 3^3.
%e A133647 a(4) = 108 = 4 * 3^3.
%t A133647 Join[{1},Flatten[NestList[9#&,{3,12},20]]] (* or *) LinearRecurrence[{0,9},{1,3,12},40] (* _Harvey P. Dale_, Aug 01 2019 *)
%Y A133647 Cf. A000244, A133566, A133646.
%K A133647 nonn,easy
%O A133647 0,2
%A A133647 _Gary W. Adamson_, Sep 19 2007
%E A133647 More terms from _Philippe Deléham_, Apr 06 2012