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 A323824 #21 Nov 26 2024 13:41:28
%S A323824 6,25,101,405,1621,6485,25941,103765,415061,1660245,6640981,26563925,
%T A323824 106255701,425022805,1700091221,6800364885,27201459541,108805838165,
%U A323824 435223352661,1740893410645,6963573642581,27854294570325,111417178281301,445668713125205
%N A323824 a(0) = 6; thereafter a(n) = 4*a(n-1) + 1.
%H A323824 Colin Barker, <a href="/A323824/b323824.txt">Table of n, a(n) for n = 0..1000</a>
%H A323824 Mike Warburton, <a href="https://arxiv.org/abs/1901.10565">Ulam-Warburton Automaton - Counting Cells with Quadratics</a>, arXiv:1901.10565 [math.CO], 2019.
%H A323824 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A323824 G.f.: (6 - 5*x) / ((1 - x)*(1 - 4*x)).
%F A323824 a(n) = (19*4^n - 1) / 3. - _Colin Barker_, Feb 01 2019
%F A323824 a(n) = A178415(7, n) = A347834(10, n-1), arrays, for n >= 1. - _Wolfdieter Lang_, Nov 29 2021
%t A323824 A323824[n_]:=(19*4^n-1)/3;Array[A323824,30,0] (* or *)
%t A323824 LinearRecurrence[{5,-4},{6,25},30] (* _Paolo Xausa_, Nov 14 2023 *)
%t A323824 NestList[4#+1&,6,30] (* _Harvey P. Dale_, Nov 26 2024 *)
%o A323824 (PARI) Vec((6 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^25)) \\ _Colin Barker_, Feb 01 2019
%o A323824 (PARI) a(n) = (19*4^n - 1) / 3 \\ _Colin Barker_, Feb 01 2019
%Y A323824 Cf. A178415, A347834.
%K A323824 nonn,easy
%O A323824 0,1
%A A323824 _N. J. A. Sloane_, Feb 01 2019