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 A114299 #10 Dec 20 2015 15:19:29
%S A114299 1,1,1,1,1,2,5,13,34,89,288,1029,3794,14113,52624,210428,883881,
%T A114299 3805858,16570925,72497060,325602364,1498899060,7017126473,
%U A114299 33185818242,157858754637,759960988368,3706528583080,18273586377144,90805138443560,453695642109973
%N A114299 First row of Modified Schroeder numbers for q=9 (A114295).
%C A114299 a(i) is the number of paths from (0,0) to (i,i) using steps of length (0,1), (1,0) and (1,1), not passing above the line y=x nor below the line y=4x/5.
%H A114299 Alois P. Heinz, <a href="/A114299/b114299.txt">Table of n, a(n) for n = 0..500</a>
%H A114299 C. Hanusa, <a href="http://people.qc.cuny.edu/faculty/christopher.hanusa/research/Documents/papers/Dissertation.pdf">A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows</a>, PhD Thesis, 2005, University of Washington, Seattle, USA.
%e A114299 The number of paths from (0,0) to (6,6) staying between the lines y=x and y=4x/5 using steps of length (0,1), (1,0) and (1,1) is a(6)=5.
%p A114299 b:= proc(x, y) option remember; `if`(y>x or y<4*x/5, 0,
%p A114299 `if`(x=0, 1, b(x, y-1)+b(x-1, y)+b(x-1, y-1)))
%p A114299 end:
%p A114299 a:= n-> b(n, n):
%p A114299 seq(a(n), n=0..35); # _Alois P. Heinz_, Apr 25 2013
%t A114299 b[x_, y_] := b[x, y] = If[y > x || y < 4*x/5, 0, If[x == 0, 1, b[x, y-1] + b[x-1, y] + b[x-1, y-1]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Dec 19 2015, after _Alois P. Heinz_ *)
%Y A114299 See also A112833-A112844 and A114292-A114298.
%K A114299 nonn
%O A114299 0,6
%A A114299 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005