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 A083324 #22 Dec 14 2024 13:47:49
%S A083324 1,3,11,45,191,813,3431,14325,59231,242973,990551,4019205,16249871,
%T A083324 65522733,263668871,1059425685,4251986111,17050860093,68332318391,
%U A083324 273716169765,1096025891951,4387588255053,17560809179111,70274609387445,281192563951391,1125052651787613
%N A083324 a(n) = 4^n - 3^n + 2^n.
%C A083324 An alternating sum of decreasing powers.
%C A083324 Binomial transform of A083323.
%H A083324 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).
%F A083324 a(n) = 2 * A053154(n) + 1.
%F A083324 G.f.: (1-6*x+10*x^2)/((1-2*x)*(1-3*x)*(1-4*x)).
%F A083324 E.g.f.: exp(4*x) - exp(3*x) + exp(2*x).
%F A083324 a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3). - _Geoffrey Critzer_, Dec 01 2013
%t A083324 Table[4^n-3^n+2^n,{n,0,23}] (* _Geoffrey Critzer_, Dec 01 2013 *)
%Y A083324 Cf. A053154, A083323.
%K A083324 nonn,easy
%O A083324 0,2
%A A083324 _Paul Barry_, Apr 27 2003