This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109241 #44 Feb 16 2025 08:32:58
%S A109241 1,110,11100,1111000,111110000,11111100000,1111111000000,
%T A109241 111111110000000,11111111100000000,1111111111000000000,
%U A109241 111111111110000000000,11111111111100000000000,1111111111111000000000000,111111111111110000000000000,11111111111111100000000000000
%N A109241 Expansion of 1/((1-10*x)*(1-100*x)).
%C A109241 a(n) has n+1 1's and n 0's. Partial sums are A109242.
%C A109241 a(n) = A171476(n) converted from decimal to binary. - _Robert Price_, Jan 19 2016
%C A109241 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 A109241 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A109241 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A109241 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A109241 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A109241 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A109241 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110,-1000)
%F A109241 a(n) = (10^(2n+1) - 10^n)/9.
%F A109241 a(n) = A006516(n+1) written in base 2. - _Omar E. Pol_, Feb 24 2008
%F A109241 a(n) = A138147(n+1)/10. - _Omar E. Pol_, Nov 08 2008
%F A109241 a(n) = 110*a(n-1) -1000*a(n-2), n>=2. - _Vincenzo Librandi_, Mar 18 2011
%F A109241 a(n) = A002275(n+1)*10^n. - _Wesley Ivan Hurt_, Jun 22 2013
%F A109241 E.g.f.: (1/9)*(10*exp(100*x) - exp(10*x)). - _G. C. Greubel_, Aug 01 2017
%p A109241 A109241 := proc(n)(10^(2*n+1)-10^n)/9 ; end proc:
%p A109241 seq(A109241(n),n=0..20) ; # _R. J. Mathar_, Mar 21 2011
%t A109241 Table[(10^(2*n+1)-10^n)/9, {n, 0, 100}] (* _Robert Price_, Feb 21 2016 *)
%t A109241 CoefficientList[Series[1/((1 - 100 x) (1 - 10 x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Feb 22 2016 *)
%o A109241 (PARI) a(n)=10^(2*n+1)/9-10^n/9 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A109241 (Magma) [10^(2*n+1)/9-10^n/9: n in [0..40]]; // _Vincenzo Librandi_, Feb 22 2016
%Y A109241 Cf. A006516, A138147.
%K A109241 easy,nonn
%O A109241 0,2
%A A109241 _Paul Barry_, Jun 23 2005