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 A251733 #26 Feb 01 2023 14:29:20
%S A251733 0,3,-18,135,-972,7047,-51030,369603,-2676888,19387755,-140418522,
%T A251733 1017000927,-7365772260,53347641903,-386377801758,2798395587675,
%U A251733 -20267773741872,146792202740307,-1063163180118690,7700108905374903,-55769122053317628,403915712468279895
%N A251733 a(n) = 3^n*A077985(n-1), A077985(-1) = 0. Irrational parts of the integers in Q(sqrt(2)) giving the length of a Lévy C-curve variant at iteration step n.
%C A251733 The rational parts are given in A251732.
%C A251733 Inspired by the Lévy C-curve, and generated using different construction rules as shown in the links.
%C A251733 The length of this variant Lévy C-curve is an integer in the real quadratic number field Q(sqrt(2)), namely L(n) = A(n) + B(n)*sqrt(2) with A(n) = A251732(n) = 3^n*A123335(n) and B(n) = a(n) = 3^n*A077985(n-1), with A077985(-1) = 0. See the construction rule and the illustration in the links.
%C A251733 The total length of the Lévy C-curve after n iterations is sqrt(2^n), also an integer in Q(sqrt(2)). The fractal dimension of the Lévy C-curve is 2, but for this modified case it is log(3)/log(1+sqrt(2)) = 1.2464774357... .
%H A251733 Colin Barker, <a href="/A251733/b251733.txt">Table of n, a(n) for n = 0..1000</a>
%H A251733 Kival Ngaokrajang, <a href="/A251732/a251732.pdf">Construction rule</a>, <a href="/A251732/a251732_1.pdf">Illustration of modified Lévy C curve</a>
%H A251733 Wikipedia, <a href="http://en.wikipedia.org/wiki/L%C3%A9vy_C_curve">Lévy C curve</a>
%H A251733 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-6,9).
%F A251733 a(n) = 3^n*A077985(n-1), A077985(-1) = 0.
%F A251733 G.f.: 3*x /(1 + 6*x - 9*x^2). See the _Colin Barker_, Dec 07 2014 program.
%F A251733 a(n) = ((3*(-1+sqrt(2)))^n - (-3*(1+sqrt(2)))^n)/(2*sqrt(2)). - _Colin Barker_, Jan 21 2017
%F A251733 E.g.f.: exp(-3*x)*sinh(3*sqrt(2)*x)/sqrt(2). - _Stefano Spezia_, Feb 01 2023
%t A251733 LinearRecurrence[{-6,9}, {0,3}, 30] (* _G. C. Greubel_, Nov 18 2017 *)
%o A251733 (PARI) concat(0, Vec(-3*x / (9*x^2-6*x-1) + O(x^100))) \\ _Colin Barker_, Dec 07 2014
%o A251733 (Magma) [Round(((3*(-1+Sqrt(2)))^n - (-3*(1+Sqrt(2)))^n)/(2*Sqrt(2))): n in [0..30]]; // _G. C. Greubel_, Nov 18 2017
%Y A251733 Cf. A123335, A077985, A251732, A017910.
%K A251733 sign,easy
%O A251733 0,2
%A A251733 _Kival Ngaokrajang_, Dec 07 2014
%E A251733 More terms from _Colin Barker_, Dec 07 2014
%E A251733 Edited: see A251732. - _Wolfdieter Lang_, Dec 07 2014