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

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.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

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

Cf. A139251, A194271, A289841, A290221, A294020.

Sequence in context: A107287 A240119 A292755 * A200267 A273308 A105790

Adjacent sequences: A294018 A294019 A294020 * A294022 A294023 A294024

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Oct 21 2017

Status

approved