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A294021
Number of elements added at n-th stage to the structure of the cellular automaton described in A294020.
10
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, 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, 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
OFFSET
0,3
COMMENTS
Essentially the first differences of A294020.
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.
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.
FORMULA
From Colin Barker, Nov 11 2017: (Start)
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)).
a(n) = a(n-6) for n > 10.
(End)
EXAMPLE
The sequence begins:
0, 1, 4, 4, 6;
The periodic tail begins:
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;
...
PROG
(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
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Omar E. Pol, Oct 21 2017
STATUS
approved