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A255047 1 together with the positive terms of A000225. 5
1, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, right border of A246674 arranged as an irregular triangle.

Essentially the same as A168604, A126646 and A000225.

Total number of lambda-parking functions induced by all partitions of n. a(0)=1: [], a(1)=1: [1], a(2)=3: [1], [2], [1,1], a(4)=7: [1], [2], [3], [1,1], [1,2], [2,1], [1,1,1]. - Alois P. Heinz, Dec 04 2015

Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 645", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 19 2017

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.

R. Stanley, Parking Functions, 2011.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Wolfram Research, Wolfram Atlas of Simple Programs

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

G.f.: (2*x^2-2*x+1)/((2*x-1)*(x-1)). - Alois P. Heinz, Feb 19 2015

E.g.f.: exp(2*x)-exp(x)+1. - Alois P. Heinz, Feb 19 2015

MATHEMATICA

CoefficientList[Series[(2 x^2 - 2 x + 1) / ((2 x - 1) (x - 1)), {x, 0, 33}], x] (* or *) Join[{1}, LinearRecurrence[{3, -2}, {1, 3}, 40]] (* Vincenzo Librandi, Jul 20 2017 *)

CROSSREFS

Cf. A000225, A011782, A028310, A246674, A253909, A265007, A265202.

Row n=1 of A263159.

Sequence in context: A126646 A000225 A225883 * A168604 A123121 A117060

Adjacent sequences:  A255044 A255045 A255046 * A255048 A255049 A255050

KEYWORD

nonn,changed

AUTHOR

Omar E. Pol, Feb 15 2015

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.