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 A289841 #40 Nov 12 2017 10:19:57 %S A289841 0,1,2,8,8,8,8,32,16,16,16,48,16,16,16,64,48,32,32,80,16,16,16,64,48, %T A289841 48,32,80,16,16,16,64,48,48,32,80,16,16,16,64,48,48,32,80,16,16,16,64, %U A289841 48,48,32,80,16,16,16,64,48,48,32,80,16,16,16,64,48,48,32,80,16,16,16,64,48,48,32,80,16,16,16,64,48 %N A289841 Number of elements added at n-th stage to the structure of the complex square cross described in A289840. %C A289841 For n = 0..17 the sequence is similar to the known toothpick sequences. %C A289841 The surprising fact is that for n >= 18 the sequence has a periodic tail. More precisely, it has period 8: repeat [32, 80, 16, 16, 16, 64, 48, 48]. This tail is in accordance with the expansion of the four arms of the cross. The tail also can be written starting from the 20th stage, with period 8: repeat [16, 16, 16, 64, 48, 48, 32, 80], (see example). %C A289841 This sequence is essentially the first differences of A289840. The behavior is similar to A290221 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 A289841 Colin Barker, <a href="/A289841/b289841.txt">Table of n, a(n) for n = 0..1000</a> %H A289841 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 A289841 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %H A289841 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1). %F A289841 G.f.: x*(1 + 2*x + 8*x^2 + 8*x^3 + 8*x^4 + 8*x^5 + 32*x^6 + 16*x^7 + 15*x^8 + 14*x^9 + 40*x^10 + 8*x^11 + 8*x^12 + 8*x^13 + 32*x^14 + 32*x^15 + 16*x^16 + 16*x^17 + 32*x^18 + 16*x^24) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)). - _Colin Barker_, Nov 12 2017 %e A289841 For n = 0..17 the sequence is 0, 1, 2, 8, 8, 8, 8, 32, 16, 16, 16, 48, 16, 16, 16, 64, 48, 32; %e A289841 Terms 18 and beyond can be arranged in a rectangular array with eight columns as shown below: %e A289841 32, 80, 16, 16, 16, 64, 48, 48; %e A289841 32, 80, 16, 16, 16, 64, 48, 48; %e A289841 32, 80, 16, 16, 16, 64, 48, 48; %e A289841 32, 80, 16, 16, 16, 64, 48, 48; %e A289841 32, 80, 16, 16, 16, 64, 48, 48; %e A289841 ... %e A289841 On the other hand, in accordance with the periodic structure of the arms of the square cross, the terms 20 and beyond can be arranged in a rectangular array with eight columns as shown below: %e A289841 16, 16, 16, 64, 48, 48, 32, 80; %e A289841 16, 16, 16, 64, 48, 48, 32, 80; %e A289841 16, 16, 16, 64, 48, 48, 32, 80; %e A289841 16, 16, 16, 64, 48, 48, 32, 80; %e A289841 16, 16, 16, 64, 48, 48, 32, 80; %e A289841 ... %o A289841 (PARI) concat(0, Vec(x*(1 + 2*x + 8*x^2 + 8*x^3 + 8*x^4 + 8*x^5 + 32*x^6 + 16*x^7 + 15*x^8 + 14*x^9 + 40*x^10 + 8*x^11 + 8*x^12 + 8*x^13 + 32*x^14 + 32*x^15 + 16*x^16 + 16*x^17 + 32*x^18 + 16*x^24) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^100))) \\ _Colin Barker_, Nov 12 2017 %Y A289841 Cf. A004767, A008584, A042963, A139250, A139251, A220500, A220501, A289840, A290221, A294021. %K A289841 nonn,tabf,easy %O A289841 0,3 %A A289841 _Omar E. Pol_, Jul 14 2017