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 A152173 #16 Nov 26 2017 04:57:50
%S A152173 1,0,1,2,4,10,23,56,138,344,870,2220,5716,14828,38717,101682,268416,
%T A152173 711810,1895432,5066030,13586082,36547534,98593064,266661162,
%U A152173 722953814,1964358938,5348367006,14589803090,39870312218,109136843138
%N A152173 a(n) is the number of Dyck paths of length n without height of peaks 1 (mod 3) and height of valleys 2 (mod 3).
%H A152173 Harvey P. Dale, <a href="/A152173/b152173.txt">Table of n, a(n) for n = 2..1000</a>
%H A152173 Shu-Chung Liu, Jun Ma, Yeong-Nan Yeh, <a href="http://dx.doi.org/10.1111/j.1467-9590.2008.00415.x">Dyck Paths with Peak- and Valley-Avoiding Sets</a>, Stud. Appl Math. 121 (3) (2008) 263-289.
%F A152173 G.f.: (1 - x - sqrt(1 - 2*x - 3*x^2 + 4*x^4))/(2(1+x)x^2).
%F A152173 Conjecture: -n*a(n) + (n-3)*a(n-1) + (5*n-12)*a(n-2) + 3*(n-3)*a(n-3) + 4*(6-n)*a(n-4) + 4*(6-n)*a(n-5) = 0. - _R. J. Mathar_, Aug 14 2012
%F A152173 G.f.: 1/x^2 - 2/x + 2/(1+x) + G(0)/x where G(k) = 1 - 1/(x + x^2/(1 + x/G(k+1))); (continued fraction, 3-step). - _Sergei N. Gladkovskii_, Nov 28 2012
%t A152173 CoefficientList[Series[(1-x-Sqrt[1-2x-3x^2+4x^4])/(2x^2 (1+x)),{x,0,30}],x] (* _Harvey P. Dale_, Feb 10 2015 *)
%Y A152173 Cf. A127389. - _R. J. Mathar_, Dec 03 2008
%K A152173 nonn
%O A152173 2,4
%A A152173 Jun Ma (majun(AT)math.sinica.edu.tw), Nov 27 2008