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 A115243 #43 May 05 2023 07:44:29
%S A115243 0,2,12,50,204,818,3276,13106,52428,209714,838860,3355442,13421772,
%T A115243 53687090,214748364,858993458,3435973836,13743895346,54975581388,
%U A115243 219902325554,879609302220,3518437208882,14073748835532,56294995342130,225179981368524,900719925474098
%N A115243 G.f.: (4*x^2 + 2*x)/(4*x^3 - x^2 - 4*x + 1).
%C A115243 Inverse Z-transform of polynomial in A112627.
%C A115243 a(n) is also the number of corners in the n-th approximation of the Hilbert Curve. The 1st Hilbert Curve approximation has 2 corners. To find a(n) given a(n - 1), look at how the n-th Hilbert Curve approximation is constructed: duplicate the (n-1)-th approximation 4 times and connect the duplicates with 3 line segments. a(n) will always be 4 * a(n - 1) corners from the 4 duplicates plus 4 new corners if n is even or 2 new corners if n is odd. - _Mikel Mcdaniel_, Jan 10 2019
%H A115243 G. C. Greubel, <a href="/A115243/b115243.txt">Table of n, a(n) for n = 0..500</a>
%H A115243 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).
%F A115243 a(n) = InverseZTransform[(1 + 2*x)/(1 - x - 16*x^2 + 16*x^3), x, n] * 2^(2*n).
%F A115243 a(n) = 5*a(n-1)-4*a(n-2) +2*(-1)^n.
%F A115243 a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). - _Gary Detlefs_ Dec 17 2010
%F A115243 a(n) = (4^(n+1)+(-1)^n)/5 - 1. - _Robert Israel_, Mar 09 2016
%F A115243 a(n) = 4*a(n-1)+3+(-1)^n. - _Mikel Mcdaniel_, Jan 10 2019
%p A115243 seq((4^(n+1)+(-1)^n)/5 - 1, n=0..100); # _Robert Israel_, Mar 09 2016
%t A115243 Table[InverseZTransform[(1 + 2*x)/(1 - x - 16*x^2 + 16*x^3), x, n]*2^( 2*n), {n, 1, 25}]
%t A115243 LinearRecurrence[{4, 1, -4}, {0, 2, 12}, 50] (* _G. C. Greubel_, Feb 07 2016 *)
%o A115243 (Magma) [(4^(n+1)+(-1)^n)/5 - 1: n in [0..25]]; // _Vincenzo Librandi_, Jan 10 2019
%o A115243 (PARI) a(n) = (bitneg(0,2*n+2)-1)\5; \\ _Kevin Ryde_, May 05 2023
%Y A115243 Cf. A112627.
%K A115243 nonn,easy
%O A115243 0,2
%A A115243 _Roger L. Bagula_, Mar 04 2006
%E A115243 Entry revised by _N. J. A. Sloane_, Dec 18 2010