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 A083316 #15 Jun 27 2025 08:19:39
%S A083316 1,5,28,167,1024,6335,39208,241967,1487584,9110975,55612888,338471567,
%T A083316 2054977744,12451139615,75314797768,454933369967,2744837485504,
%U A083316 16545254288255,99652801745848,599823577977167,3608476467634864,21698537291452895,130429626637289128,783769805647653167
%N A083316 a(n) = (2*6^n - (5^n - 3^n))/2.
%C A083316 Binomial transform of A083315.
%H A083316 Paolo Xausa, <a href="/A083316/b083316.txt">Table of n, a(n) for n = 0..1000</a>
%H A083316 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-63,90).
%F A083316 G.f.: (1-9x+21x^2)/((1-3x)(1-5x)(1-6x)).
%F A083316 E.g.f.: (2*exp(6x) - exp(5x) + exp(3x))/2.
%F A083316 a(n) = 14*a(n-1) - 63*a(n-2) + 90*a(n-3). - _Wesley Ivan Hurt_, Jun 26 2025
%t A083316 A083316[n_] := 6^n - (5^n - 3^n)/2; Array[A083316, 25, 0] (* or *)
%t A083316 LinearRecurrence[{14, -63, 90}, {1, 5, 28}, 25] (* _Paolo Xausa_, Jun 27 2025 *)
%Y A083316 Cf. A083315.
%K A083316 easy,nonn
%O A083316 0,2
%A A083316 _Paul Barry_, Apr 24 2003