cp's OEIS Frontend

A294021 Number of elements added at n-th stage to the structure of the cellular automaton described in A294020.

%I A294021 #27 Nov 12 2017 10:20:11
%S A294021 0,1,4,4,6,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,
%T A294021 16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,
%U A294021 22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22,8,4,14,24,16,22
%N A294021 Number of elements added at n-th stage to the structure of the cellular automaton described in A294020.
%C A294021 Essentially the first differences of A294020.
%C A294021 The sequence starts with 0, 1, 4, 4, 6. For n >= 5 the sequence has a periodic tail. More precisely, it has period 6: repeat [8, 4, 14, 24, 16, 22]. This tail is in accordance with the expansion of the two arms of the structure.
%C A294021 The behavior is similar to A289841 and A290221 in the sense that these three sequences from cellular automata have the property that after the initial terms the continuation is a periodic sequence.
%H A294021 Colin Barker, <a href="/A294021/b294021.txt">Table of n, a(n) for n = 0..1000</a>
%H A294021 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 A294021 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A294021 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A294021 From _Colin Barker_, Nov 11 2017: (Start)
%F A294021 G.f.: x*(1 + 4*x + 4*x^2 + 6*x^3 + 8*x^4 + 4*x^5 + 13*x^6 + 20*x^7 + 12*x^8 + 16*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).
%F A294021 a(n) = a(n-6) for n > 10.
%F A294021 (End)
%e A294021 The sequence begins:
%e A294021 0, 1, 4, 4, 6;
%e A294021 The periodic tail begins:
%e A294021 8, 4, 14, 24, 16, 22;
%e A294021 8, 4, 14, 24, 16, 22;
%e A294021 8, 4, 14, 24, 16, 22,
%e A294021 8, 4, 14, 24, 16, 22;
%e A294021 8, 4, 14, 24, 16, 22;
%e A294021 ...
%o A294021 (PARI) concat(0, Vec(x*(1 + 4*x + 4*x^2 + 6*x^3 + 8*x^4 + 4*x^5 + 13*x^6 + 20*x^7 + 12*x^8 + 16*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) + O(x^100))) \\ _Colin Barker_, Nov 11 2017
%Y A294021 Cf. A139251, A194271, A289841, A290221, A294020.
%K A294021 nonn,tabf,easy
%O A294021 0,3
%A A294021 _Omar E. Pol_, Oct 21 2017