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 A200676 #58 Jul 29 2025 14:39:09
%S A200676 1,0,0,1,5,22,96,419,1829,7984,34852,152137,664113,2899006,12654828,
%T A200676 55241235,241140697,1052634608,4594992184,20058197793,87558647021,
%U A200676 382213633910,1668450426280,7283169876691,31792711738525,138782499488832,605817532105276
%N A200676 Expansion of g.f. -(3*x^2-5*x+1)/(x^3-3*x^2+5*x-1).
%C A200676 _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 A200676 The sequence without the first 3 entries (1, 5, 22, 96,...) are the partial sums of the partial sums of A049086. - _R. J. Mathar_, Jul 20 2025
%H A200676 Alois P. Heinz, <a href="/A200676/b200676.txt">Table of n, a(n) for n = 0..500</a>
%H A200676 D. Birmajer, J. B. Gil, M. D. Weiner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Gil/gil6.html">On the Enumeration of Restricted Words over a Finite Alphabet</a>, J. Int. Seq. 19 (2016) # 16.1.3 , example 14.
%H A200676 Sela Fried, Toufik Mansour, and Mark Shattuck, <a href="https://arxiv.org/abs/2504.03013">Counting k-ary words by number of adjacency differences of a prescribed size</a>, arXiv:2504.03013 [math.CO], 2025. See p. 7.
%H A200676 Milan Janjić, <a href="https://www.emis.de/journals/JIS/VOL21/Janjic2/janjic103.html">Pascal Matrices and Restricted Words</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
%H A200676 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 A200676 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3,1).
%F A200676 G.f.: -(3*x^2-5*x+1)/(x^3-3*x^2+5*x-1).
%F A200676 Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-3,5]^n.
%p A200676 a:= n-> (<<0|1|0>, <0|0|1>, <1|-3|5>>^n)[1, 1]:
%p A200676 seq(a(n), n=0..30);
%t A200676 CoefficientList[Series[-(3 x^2 - 5 x + 1)/(x^3 - 3 x^2 + 5 x - 1), {x, 0, 26}], x] (* _Michael De Vlieger_, Sep 04 2018 *)
%t A200676 LinearRecurrence[{5,-3,1},{1,0,0},40] (* _Harvey P. Dale_, Aug 18 2021 *)
%Y A200676 Cf. A049086, A200739.
%K A200676 nonn,easy
%O A200676 0,5
%A A200676 _Alois P. Heinz_, Nov 21 2011