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 A097813 #34 Sep 08 2022 08:45:14
%S A097813 1,2,6,16,38,84,178,368,750,1516,3050,6120,12262,24548,49122,98272,
%T A097813 196574,393180,786394,1572824,3145686,6291412,12582866,25165776,
%U A097813 50331598,100663244,201326538,402653128,805306310,1610612676,3221225410,6442450880,12884901822,25769803708
%N A097813 a(n) = 3*2^n - 2*n - 2.
%C A097813 An elephant sequence, see A175654. For the corner squares four A[5] vectors, with decimal values 58, 154, 178 and 184, lead to this sequence. For the central square these vectors lead to the companion sequence A033484. - _Johannes W. Meijer_, Aug 15 2010
%C A097813 a(n) is also the number of order-preserving partial isometries of an n-chain, i.e., the row sums of A183153 and A183154. - _Abdullahi Umar_, Dec 28 2010
%H A097813 Harvey P. Dale, <a href="/A097813/b097813.txt">Table of n, a(n) for n = 0..1000</a>
%H A097813 F. Al-Kharousi, R. Kehinde and A. Umar, <a href="http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p365.pdf">Combinatorial results for certain semigroups of partial isometries of a finite chain</a>, The Australasian Journal of Combinatorics, Volume 58 (3) (2014), 363-375.
%H A097813 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A097813 G.f.: (1 - 2*x + 3*x^2)/((1-x)^2*(1-2*x)).
%F A097813 a(n) = 2*a(n-1) + 2*n - 2, for n>0, with a(0)=1.
%F A097813 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F A097813 From _G. C. Greubel_, Dec 30 2021: (Start)
%F A097813 a(n) = 2^n + 2*A000295(n).
%F A097813 E.g.f.: 3*exp(2*x) - 2*(1 + x)*exp(x). (End)
%t A097813 Table[3 2^n-2n-2,{n,0,40}] (* or *) LinearRecurrence[{4,-5,2},{1,2,6},40] (* _Harvey P. Dale_, Oct 25 2011 *)
%o A097813 (PARI) a(n)=3*2^n-2*n-2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A097813 (Magma) [3*2^n -2*(n+1): n in [0..40]]; // _G. C. Greubel_, Dec 30 2021
%o A097813 (Sage) [3*2^n -2*(n+1) for n in (0..40)] # _G. C. Greubel_, Dec 30 2021
%Y A097813 Cf. A000295, A033484, A079583, A175654, A183153, A183154.
%K A097813 easy,nonn
%O A097813 0,2
%A A097813 _Paul Barry_, Aug 25 2004