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 A290221 #28 Dec 31 2018 18:20:05
%S A290221 0,2,4,4,8,8,8,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,
%T A290221 12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,
%U A290221 16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12,8,16,12
%N A290221 Number of elements added at n-th stage to the structure of the narrow cross described in A290220.
%C A290221 For n = 0..6 the sequence is similar to some toothpick sequences.
%C A290221 The surprising fact is that for n >= 7 the sequence has periodic tail. More precisely, it has period 3: repeat [8, 16, 12]. This tail is in accordance with the expansion of the four arms of the cross.
%C A290221 This is essentially the first differences of A290221. The behavior is similar to A289841 and A294021 in the sense that these three sequences from cellular automata have the property that after the initial terms the continuation is a periodic sequence. - _Omar E. Pol_, Oct 29 2017
%H A290221 Colin Barker, <a href="/A290221/b290221.txt">Table of n, a(n) for n = 0..1000</a>
%H A290221 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H A290221 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A290221 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A290221 G.f.: 2*x*(1 + 2*x + 2*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8) / ((1 - x)*(1 + x + x^2)). - _Colin Barker_, Nov 12 2017
%e A290221 For n = 0..6 the sequence is: 0, 2, 4, 4, 8, 8, 8;
%e A290221 Terms 7 and beyond can be arranged in a rectangular array with three columns as shown below:
%e A290221 8, 16, 12;
%e A290221 8, 16, 12;
%e A290221 8, 16, 12;
%e A290221 8, 16, 12;
%e A290221 ...
%t A290221 LinearRecurrence[{0,0,1},{0,2,4,4,8,8,8,8,16,12},90] (* _Harvey P. Dale_, Dec 31 2018 *)
%o A290221 (PARI) concat(0, Vec(2*x*(1 + 2*x + 2*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8) / ((1 - x)*(1 + x + x^2)) + O(x^100))) \\ _Colin Barker_, Nov 12 2017
%Y A290221 Cf. A004767, A008584, A042963, A139250, A139251, A220500, A220501, A289841 (a more complex cross), A290220, A294021.
%K A290221 nonn,tabf,easy
%O A290221 0,2
%A A290221 _Omar E. Pol_, Jul 24 2017