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 A094618 #18 Mar 06 2025 20:08:51
%S A094618 2,7,22,69,216,671,2066,6313,19180,58035,175110,527357,1586144,
%T A094618 4766599,14316154,42981201,129009108,387158363,1161737198,3485735845,
%U A094618 10458256072,31376865327,94134790242,282412759289,847255055036,2541798719491,7625463267286,22876524019533
%N A094618 a(n) = 3^(n+1) - 2^(n+1) + n + 1.
%C A094618 Row sums of A094617.
%H A094618 Robert Israel, <a href="/A094618/b094618.txt">Table of n, a(n) for n = 0..2092</a>
%H A094618 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6).
%F A094618 a(n) = 2*a(n-1) + 1 - n + 3^n, a(0) = 2.
%F A094618 G.f.: (2-7*x+7*x^2)/(1-7*x+17*x^2-17*x^3+6*x^4). - _Robert Israel_, Jul 22 2018
%F A094618 From _Elmo R. Oliveira_, Mar 06 2025: (Start)
%F A094618 E.g.f.: exp(x)*(1 + x + 3*exp(2*x) - 2*exp(x)).
%F A094618 a(n) = 7*a(n-1) - 17*a(n-2) + 17*a(n-3) - 6*a(n-4). (End)
%p A094618 seq(3^(n+1) - 2^(n+1) + n + 1, n=0..100); # _Robert Israel_, Jul 22 2018
%t A094618 Table[3^(n+1)-2^(n+1)+n+1,{n,0,30}] (* or *) LinearRecurrence[{7,-17,17,-6},{2,7,22,69},30] (* _Harvey P. Dale_, Oct 11 2022 *)
%o A094618 (PARI) a(n) = 3^(n+1) - 2^(n+1) + n + 1; \\ _Michel Marcus_, Jun 05 2016
%Y A094618 Cf. A094617.
%K A094618 nonn,easy
%O A094618 0,1
%A A094618 _Clark Kimberling_, May 14 2004
%E A094618 New definition from _Ralf Stephan_, Dec 01 2004