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 A248225 #17 Jul 12 2025 19:22:04
%S A248225 0,3,27,189,1215,7533,45927,277749,1673055,10058013,60407127,
%T A248225 362619909,2176250895,13059099693,78359381127,470170635669,
%U A248225 2821066860735,16926530304573,101559569247927,609358577749029,3656154953278575,21936940180024653
%N A248225 a(n) = 6^n - 3^n.
%H A248225 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-18).
%F A248225 G.f.: 3*x/((1-3*x)*(1-6*x)).
%F A248225 a(n) = 9*a(n-1) - 18*a(n-2).
%F A248225 a(n) = 3^n*(2^n - 1) = A000244(n)*A000225(n).
%F A248225 E.g.f.: 2*exp(9*x/2)*sinh(3*x/2). - _Elmo R. Oliveira_, Mar 31 2025
%t A248225 Table[6^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[3 x / ((1 - 3 x) (1 - 6 x)), {x, 0, 30}], x]
%t A248225 LinearRecurrence[{9,-18},{0,3},30] (* _Harvey P. Dale_, Jul 12 2025 *)
%o A248225 (Magma) [6^n-3^n: n in [0..30]];
%Y A248225 Cf. sequences of the form k^n-3^n: A005061 (k=4), A005058 (k=5), this sequence (k=6), A190541 (k=7), A190543 (k=8), A059410 (k=9), A248226 (k=10), A139741 (k=11).
%Y A248225 Cf. A000225, A000244.
%K A248225 nonn,easy
%O A248225 0,2
%A A248225 _Vincenzo Librandi_, Oct 04 2014