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 A109242 #28 Dec 07 2019 12:18:25 %S A109242 1,111,11211,1122211,112232211,11223332211,1122334332211, %T A109242 112233444332211,11223344544332211,1122334455544332211, %U A109242 112233445565544332211,11223344556665544332211,1122334455667665544332211,112233445566777665544332211,11223344556677877665544332211 %N A109242 Expansion of 1/((1-x)(1-10x)(1-100x)). %C A109242 Partial sums of A109241. %H A109242 Andrew Howroyd, <a href="/A109242/b109242.txt">Table of n, a(n) for n = 0..100</a> %H A109242 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000). %F A109242 a(n) = 10^(2*n+3)/891 - 10^(n+1)/81 + 1/891. %F A109242 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3). %F A109242 a(n) = 110*a(n-1) - 1000*a(n-2) + 1, n >= 2. - _Vincenzo Librandi_, Mar 18 2011 %e A109242 The numbers of 1's, 2's, 3's etc. appearing occur according to %e A109242 1:1,3,4,4,4,4,4,4,... %e A109242 2:0,0,1,3,4,4,4,4,... %e A109242 3:0,0,0,0,1,3,4,4,... %e A109242 4:0,0,0,0,0,0,1,3,... etc. up to term 17, where 9->10 etc. changes the pattern. %o A109242 (Sage) [gaussian_binomial(n,2,10) for n in range(2,14)] # _Zerinvary Lajos_, May 27 2009 %o A109242 (PARI) a(n) = {10^(2*n+3)/891 - 10^(n+1)/81 + 1/891} \\ _Andrew Howroyd_, Nov 08 2019 %K A109242 easy,nonn %O A109242 0,2 %A A109242 _Paul Barry_, Jun 23 2005 %E A109242 Terms a(12) and beyond from _Andrew Howroyd_, Nov 08 2019