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

0,2

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

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).

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

Example

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;
...

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A237264 A265560 A265544 * A098820 A296613 A062383

Adjacent sequences: A290218 A290219 A290220 * A290222 A290223 A290224

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Jul 24 2017

Status

approved