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 A353580 #21 Mar 14 2025 17:09:45
%S A353580 0,2,3,7,16,38,91,219,528,1274,3075,7423,17920,43262,104443,252147,
%T A353580 608736,1469618,3547971,8565559,20679088,49923734,120526555,290976843,
%U A353580 702480240,1695937322,4094354883,9884647087,23863649056,57611945198,139087539451,335787024099,810661587648
%N A353580 a(n) = 2*a(n-1) + a(n-2) - 1, with a(0) = 0 and a(1) = 2.
%H A353580 Paul K. Stockmeyer, <a href="/A353580/b353580.txt">Table of n, a(n) for n = 0..1000</a>
%H A353580 Andreas M. Hinz and Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Hinz/hinz5.html">Precious Metal Sequences and Sierpinski-Type Graphs</a>, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
%H A353580 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1).
%F A353580 a(n) = (1/4)((2*s - 1)*(1 + s)^n - (2*s + 1)*(1 - s)^n + 2) where s = sqrt(2).
%F A353580 G.f.: -x*(3*x-2)/((x-1)*(x^2+2*x-1)). - _Alois P. Heinz_, May 03 2022
%F A353580 E.g.f.: exp(x)*(1 - cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x))/2. - _Stefano Spezia_, May 03 2022
%t A353580 nxt[{a_,b_}]:={b,2b+a-1}; NestList[nxt,{0,2},40][[;;,1]] (* or *) LinearRecurrence[{3,-1,-1},{0,2,3},40] (* _Harvey P. Dale_, Mar 14 2025 *)
%K A353580 nonn,easy
%O A353580 0,2
%A A353580 _Paul K. Stockmeyer_, May 03 2022