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Number of elements added at n-th stage to the structure of the cellular automaton described in A294020.
10

%I #27 Nov 12 2017 10:20:11

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

%C Essentially the first differences of A294020.

%C 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 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 Colin Barker, <a href="/A294021/b294021.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F From _Colin Barker_, Nov 11 2017: (Start)

%F 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 a(n) = a(n-6) for n > 10.

%F (End)

%e The sequence begins:

%e 0, 1, 4, 4, 6;

%e The periodic tail begins:

%e 8, 4, 14, 24, 16, 22;

%e 8, 4, 14, 24, 16, 22;

%e 8, 4, 14, 24, 16, 22,

%e 8, 4, 14, 24, 16, 22;

%e 8, 4, 14, 24, 16, 22;

%e ...

%o (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 Cf. A139251, A194271, A289841, A290221, A294020.

%K nonn,tabf,easy

%O 0,3

%A _Omar E. Pol_, Oct 21 2017