A290221 Number of elements added at n-th stage to the structure of the narrow cross described in A290220.

0, 2, 4, 4, 8, 8, 8, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12, 8, 16, 12

Offset: 0

Author

Omar E. Pol, Jul 24 2017

Keywords

• nonn
• tabf
• easy

Comments

For n = 0..6 the sequence is similar to some toothpick sequences.

The surprising fact is that for n >= 7 the sequence has periodic tail. More precisely, it has period 3: repeat [8, 16, 12]. This tail is in accordance with the expansion of the four arms of the cross.

This is essentially the first differences of A290221. The behavior is similar to A289841 and A294021 in the sense that these three sequences from cellular automata have the property that after the initial terms the continuation is a periodic sequence. - Omar E. Pol, Oct 29 2017

Examples

			For n = 0..6 the sequence is: 0, 2, 4, 4, 8, 8, 8;
Terms 7 and beyond can be arranged in a rectangular array with three columns as shown below:
8, 16, 12;
8, 16, 12;
8, 16, 12;
8, 16, 12;
...
		

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 (0,0,1).

Crossrefs

Cf. A004767, A008584, A042963, A139250, A139251, A220500, A220501, A289841 (a more complex cross), A290220, A294021.

Programs

Mathematica

LinearRecurrence[{0,0,1},{0,2,4,4,8,8,8,8,16,12},90] (* Harvey P. Dale, Dec 31 2018 *)

PARI

concat(0, Vec(2*x*(1 + 2*x + 2*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8) / ((1 - x)*(1 + x + x^2)) + O(x^100))) \\ Colin Barker, Nov 12 2017

Formula

G.f.: 2*x*(1 + 2*x + 2*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8) / ((1 - x)*(1 + x + x^2)). - Colin Barker, Nov 12 2017