A140252 Inverse binomial transform of A140420.

0, 1, 1, 7, 7, 31, 31, 127, 127, 511, 511, 2047, 2047, 8191, 8191, 32767, 32767, 131071, 131071, 524287, 524287, 2097151, 2097151, 8388607, 8388607, 33554431, 33554431, 134217727, 134217727, 536870911, 536870911

Offset

0,4

Comments

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 673", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 23 2017

References

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

Links

Harvey P. Dale, 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

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 (1, 4, -4).

Formula

a(2n+1) = a(2n+2)= A083420(n).

a(n+1)-2a(n) = (-1)^n*A014551(n), n>0.

a(n+1)-2a(n)-1 = 2*(-1)^n*A131577(n).

O.g.f.: x(1+2x^2)/((2x-1)(1+2x)(x-1)). - R. J. Mathar, Aug 02 2008

a(n) = a(n-1)+4*a(n-2)-4*a(n-3), a(0)=0, a(1)=1, a(2)=1, a(3)=7. - Harvey P. Dale, May 28 2012

Mathematica

Join[{0}, LinearRecurrence[{1, 4, -4}, {1, 1, 7}, 30]] (* Harvey P. Dale, May 28 2012 *)

Crossrefs

Sequence in context: A188274 A255281 A255283 * A095343 A286830 A286862

Adjacent sequences: A140249 A140250 A140251 * A140253 A140254 A140255

Keyword

nonn

Author

Paul Curtz, Jun 23 2008

Extensions

Edited and extended by R. J. Mathar, Aug 02 2008

Status

approved