OFFSET
0,2
COMMENTS
a(n) is the smallest even number with digits in {0,1} having digit sum n; in other words, the base 10 reading of the binary string of A000918(n). Cf. A069532. - Jason Kimberley, Nov 02 2011
Also, except for a(0), the binary representation of the diagonal from the corner to the origin 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..100
Robert Price, Diagrams of first 20 stages of the Cellular Automata.
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 linear recurrences with constant coefficients, signature (11,-10).
FORMULA
a(n) = (10/9)*(10^n-1), with n>=0.
a(n) = Sum_{k=1..n} 10^k.
Repunits times 10: a(n) = 10 * A002275(n). - Reinhard Zumkeller, Feb 05 2012
From Stefano Spezia, Sep 15 2023: (Start)
O.g.f.: 10*x/((1 - x)*(1 - 10*x)).
E.g.f.: 10*exp(x)*(exp(9*x) - 1)/9. (End)
MATHEMATICA
NestList[10*(# + 1) &, 0, 25] (* Paolo Xausa, Jul 17 2024 *)
PROG
(Magma) [-10/9+(10/9)*10^n: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011
(Haskell)
a105279 n = a105279_list !! n
a105279_list = iterate ((* 10) . (+ 1)) 0
-- Reinhard Zumkeller, Feb 05 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexandre Wajnberg, Apr 25 2005
STATUS
approved