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 A200752 #39 Apr 25 2025 12:27:25 %S A200752 1,0,0,1,3,8,22,61,169,468,1296,3589,9939,27524,76222,211081,584545, %T A200752 1618776,4482864,12414361,34378995,95205488,263651830,730128997, %U A200752 2021940649,5599344780,15506222688,42941263933,118916913891,329315700428,911971451326,2525515567441 %N A200752 Expansion of (-x^2 + 3*x - 1)/(x^3 - x^2 + 3*x - 1). %C A200752 _Peter A. Lawrence_ (see links) has posted a challenge to find a 3x3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found. %C A200752 a(n+3) is the number of ternary strings of length n in which the number of substrings of the form 0011 equals the number of substrings of the form 11. - _John M. Campbell_, Nov 02 2013 %H A200752 Alois P. Heinz, <a href="/A200752/b200752.txt">Table of n, a(n) for n = 0..2263</a> %H A200752 Peter Lawrence et al., <a href="https://web.archive.org/web/20220127112002/http://list.seqfan.eu/pipermail/seqfan/2011-November/008535.html">sequence challenge</a> and follow-up messages on the SeqFan list, Nov 21 2011 %H A200752 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,1) %F A200752 G.f.: (-x^2+3*x-1)/(x^3-x^2+3*x-1). %F A200752 Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-1,3]^n. %F A200752 a(n) = 3*a(n-1) -a(n-2) +a(n-3) with a(0)=1, a(1)=0, a(2)=0. - _Taras Goy_, Jul 23 2017 %p A200752 a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|3>>^n)[1, 1]: %p A200752 seq(a(n), n=0..50); %Y A200752 Cf. A200676, A200739, A200715. %K A200752 nonn,easy %O A200752 0,5 %A A200752 _Alois P. Heinz_, Nov 21 2011