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A140252
Inverse binomial transform of A140420.
2
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.
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
KEYWORD
nonn
AUTHOR
Paul Curtz, Jun 23 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Aug 02 2008
STATUS
approved