Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #43 Sep 08 2022 08:45:19
%S 1,110,11100,1111000,111110000,11111100000,1111111000000,
%T 111111110000000,11111111100000000,1111111111000000000,
%U 111111111110000000000,11111111111100000000000,1111111111111000000000000,111111111111110000000000000,11111111111111100000000000000
%N Expansion of 1/((1-10*x)*(1-100*x)).
%C a(n) has n+1 1's and n 0's. Partial sums are A109242.
%C a(n) = A171476(n) converted from decimal to binary. - _Robert Price_, Jan 19 2016
%C Also the binary representation of the n-th iteration of the elementary cellular automaton starting with a single ON (black) cell for Rules 206 and 238. - _Robert Price_, Feb 21 2016
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110,-1000)
%F a(n) = (10^(2n+1) - 10^n)/9.
%F a(n) = A006516(n+1) written in base 2. - _Omar E. Pol_, Feb 24 2008
%F a(n) = A138147(n+1)/10. - _Omar E. Pol_, Nov 08 2008
%F a(n) = 110*a(n-1) -1000*a(n-2), n>=2. - _Vincenzo Librandi_, Mar 18 2011
%F a(n) = A002275(n+1)*10^n. - _Wesley Ivan Hurt_, Jun 22 2013
%F E.g.f.: (1/9)*(10*exp(100*x) - exp(10*x)). - _G. C. Greubel_, Aug 01 2017
%p A109241 := proc(n)(10^(2*n+1)-10^n)/9 ; end proc:
%p seq(A109241(n),n=0..20) ; # _R. J. Mathar_, Mar 21 2011
%t Table[(10^(2*n+1)-10^n)/9, {n, 0, 100}] (* _Robert Price_, Feb 21 2016 *)
%t CoefficientList[Series[1/((1 - 100 x) (1 - 10 x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Feb 22 2016 *)
%o (PARI) a(n)=10^(2*n+1)/9-10^n/9 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [10^(2*n+1)/9-10^n/9: n in [0..40]]; // _Vincenzo Librandi_, Feb 22 2016
%Y Cf. A006516, A138147.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 23 2005