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

Author

Omar E. Pol, Oct 21 2017

Keywords

• nonn
• tabf
• easy

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.

Examples

			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;
...
		

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).

Crossrefs

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

Programs

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

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)