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 A268402 #8 Oct 07 2016 10:22:39 %S A268402 1,7,40,204,977,4493,20091,88025,379766,1618898,6835636,28640302, %T A268402 119236085,493772409,2035611612,8359873866,34219553297,139672169795, %U A268402 568675783762,2310315996126,9367885987455,37920179012135,153263612914150,618611076034828,2493830719572639,10042451847789161 %N A268402 Number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the right exactly four times. %C A268402 This sequence is related to paired pattern P_2 in Pan and Remmel's link. %C A268402 By symmetry, it is also the number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the left exactly four times. %H A268402 Ran Pan and Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016. %F A268402 G.f.: -((-1 + f(x))^5*x^3*(-1 + f(x) + 2*x))/(2*(1 - f(x) + (-5 + f(x))*x)^5), where f(x) = sqrt(1 - 4*x). %F A268402 Conjecture: -(n-3)*(n-5)*(55*n-618)*a(n) +(-55*n^3-840*n^2+6969*n-5742)*a(n-1) %F A268402 +(3135*n^3 -37532*n^2 +138815*n -163614)*a(n-2) +(-7645*n^3 +93072*n^2 -343985*n +391386)*a(n-3) -18*(n-3)*(55*n-126)*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Oct 07 2016 %Y A268402 Cf. A268400, A268401. %K A268402 nonn %O A268402 5,2 %A A268402 _Ran Pan_, Feb 03 2016