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 A080935 #15 Jul 03 2024 12:46:33 %S A080935 1,1,2,1,4,5,1,8,13,14,1,16,34,41,42,1,32,89,122,131,132,1,64,233,365, %T A080935 417,428,429,1,128,610,1094,1341,1416,1429,1430,1,256,1597,3281,4334, %U A080935 4744,4846,4861,4862,1,512,4181,9842,14041,16016,16645,16778,16795 %N A080935 Triangle read by rows of number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2n steps with all values less than or equal to k. %C A080935 T(n,k) is the number of different out-stack sequences of n elements to be pushed into a stack of size k. E.g. T(3,2) = 4 since the 4 possible out-stack sequences are 123, 132, 213, 231; 321 is not allowed since it requires a stack of size 3. - _Jianing Song_, Oct 28 2021 %H A080935 Vince White, <a href="https://digitalcommons.georgiasouthern.edu/etd/2799">Enumeration of Lattice Paths with Restrictions</a>, (2024). Electronic Theses and Dissertations. 2799. See pp. 20, 25. %F A080935 For 1<=k<=n, T(n, k) =A080934(n, k) =T(n, k-1)+A080936(n, k). %e A080935 Rows start: %e A080935 1; %e A080935 1,2; %e A080935 1,4,5; %e A080935 1,8,13,14; %e A080935 1,16,34,41,42; %e A080935 ... %e A080935 T(3,2)=4 since the paths of length 2*3 (7 points) with all values less than or equal to 2 can take the routes 0101010, 0101210, 0121010 or 0121210, but not 0123210. %Y A080935 Cf. A000108, A079214, A080934, A080936. %K A080935 nonn,tabl %O A080935 1,3 %A A080935 _Henry Bottomley_, Feb 25 2003