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 A168607 #54 Nov 09 2023 12:15:54
%S A168607 3,5,11,29,83,245,731,2189,6563,19685,59051,177149,531443,1594325,
%T A168607 4782971,14348909,43046723,129140165,387420491,1162261469,3486784403,
%U A168607 10460353205,31381059611,94143178829,282429536483,847288609445
%N A168607 a(n) = 3^n + 2.
%C A168607 Second bisection is A134752.
%C A168607 It appears that if s(n) is a first order rational sequence of the form s(1)=5, s(n)= (2*s(n-1)+1)/(s(n-1)+2),n>1, then s(n)= a(n)/(a(n)-4), n>1. - _Gary Detlefs_, Nov 16 2010
%C A168607 Mahler exhibits this sequence with n>=1 as a proof that there exists an infinite number of x coprime to 3, such that x belongs to A125293 and x^2 belongs to A005836. - _Michel Marcus_, Nov 12 2012
%H A168607 Vincenzo Librandi, <a href="/A168607/b168607.txt">Table of n, a(n) for n = 0..1000</a>
%H A168607 Gennady Eremin, <a href="https://arxiv.org/abs/2012.12675">Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind</a>, arXiv:2012.12675 [math.CO], 2020.
%H A168607 Kurt Mahler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa53/aa5316.pdf">The representation of squares to the base 3</a>, Acta Arith. Vol. 53, Issue 1 (1989), p. 99-106.
%H A168607 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A168607 a(n) = 3*a(n-1) - 4, a(0) = 3.
%F A168607 a(n+1) - a(n) = A008776(n).
%F A168607 a(n+2) - a(n) = A005051(n).
%F A168607 a(n) = A034472(n)+1 = A000244(n)+2 = A024023(n)+3 = A168609(n)-2 = A168610(n)-3.
%F A168607 G.f.: (3 - 7*x)/((1 - x)*(1 - 3*x)).
%F A168607 a(n) = 4*a(n-1) - 3*a(n-2), a(0) = 3, a(1) = 5. - _Vincenzo Librandi_, Feb 06 2013
%F A168607 E.g.f.: exp(3*x) + 2*exp(x). - _Elmo R. Oliveira_, Nov 09 2023
%p A168607 A168607:=n->3^n + 2; seq(A168607(n), n=0..30); # _Wesley Ivan Hurt_, Mar 21 2014
%t A168607 CoefficientList[Series[(3 - 7 x)/((1-x) (1-3 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 06 2013 *)
%t A168607 NestList[3 # - 4 & , 3, 25] (* _Bruno Berselli_, Feb 06 2013 *)
%o A168607 (Magma) [3^n+2: n in [0..30]];
%o A168607 (PARI) a(n)=3^n+2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A168607 Cf. A008776 (2*3^n), A005051 (8*3^n), A034472 (3^n+1), A000244 (powers of 3), A024023 (3^n-1), A168609 (3^n+4), A168610 (3^n+5), A134752 (3^(2*n-1)+2).
%K A168607 nonn,easy
%O A168607 0,1
%A A168607 _Vincenzo Librandi_, Dec 01 2009
%E A168607 Edited by _Klaus Brockhaus_, Apr 13 2010
%E A168607 Further edited by _N. J. A. Sloane_, Aug 10 2010