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 A101692 #29 Aug 04 2025 11:36:39
%S A101692 1,1,5,1,5,17,85,1,5,17,85,257,1285,4369,21845,1,5,17,85,257,1285,
%T A101692 4369,21845,65537,327685,1114129,5570645,16843009,84215045,286331153,
%U A101692 1431655765,1,5,17,85,257,1285,4369,21845,65537,327685,1114129,5570645,16843009,84215045
%N A101692 A modular binomial sum transform of 2^n.
%C A101692 a(2^n) is 1, 5, 5, 5, 5, ...
%C A101692 a(2^n+1) is 5, 1, 17, 17, 17, ...
%C A101692 a(2*(2^n+1)) is 5, 85, 85, 85, ...
%C A101692 a(2^n)*a(2^n+1) is 5, 5, 85, 85, 85, ...
%C A101692 Also, decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 4", based on the 5-celled von Neumann neighborhood. Initialized with a single black (ON) cell at stage zero. - _Robert Price_, Nov 03 2016
%D A101692 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A101692 Stefano Spezia, <a href="/A101692/b101692.txt">Table of n, a(n) for n = 0..1500</a>
%H A101692 Robert Price, <a href="/A101692/a101692.tmp.txt">Diagrams of first 20 stages of the cellular automaton</a>
%H A101692 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%H A101692 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A101692 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A101692 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A101692 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A101692 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A101692 a(n) = Sum_{k=0..n} (binomial(2*n+2, k) mod 2)*2^k.
%F A101692 a(n) = Sum_{k=0..n} A128937(n, k)*2^(n-k). - _Philippe Deléham_, Oct 09 2007
%t A101692 a[n_]:= Sum[Mod[Binomial[2*n+2, k],2]*2^k,{k,0,n}]; Array[a,43,0] (* _Stefano Spezia_, Aug 04 2025 *)
%Y A101692 Cf. A001045, A048896.
%Y A101692 Cf. A277916, A277917, A277918.
%K A101692 nonn,easy
%O A101692 0,3
%A A101692 _Paul Barry_, Dec 11 2004