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 A243831 #9 Jan 24 2019 16:09:36 %S A243831 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,42,0,0,0,0,0,42,0,0,0,0,0,0, %T A243831 1,0,0,0,0,0,0,0,0,15,0,0,0,0,0,0,0,0,1,105,0,0,0,0,0,0,0,0,0,21,490, %U A243831 0,0,0,0,0,0,0,0,1,0,196,1764,0,0,0,0,0,0,0,0,0,6,0,1176,5292,0,0,0,0,0,0,0,0,0,0,42,0,5292,13860,0,0 %N A243831 Number A(n,k) of Dyck paths of semilength n having exactly five (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of k, where 1=U=(1,1) and 0=D=(1,-1); square array A(n,k), n>=0, k>=0, read by antidiagonals. %H A243831 Alois P. Heinz, <a href="/A243831/b243831.txt">Antidiagonals n = 0..140, flattened</a> %e A243831 Square array A(n,k) begins: %e A243831 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 42, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243831 0, 0, 15, 1, 0, 1, 0, 0, 0, 0, 1, ... %e A243831 0, 0, 105, 21, 0, 6, 0, 1, 0, 0, 1, ... %e A243831 0, 0, 490, 196, 0, 42, 0, 8, 0, 0, 13, ... %e A243831 0, 0, 1764, 1176, 0, 224, 0, 63, 0, 0, 52, ... %e A243831 0, 0, 5292, 5292, 42, 1134, 42, 390, 0, 0, 244, ... %Y A243831 Main diagonal gives A243774 or column k=5 of A243752. %Y A243831 Cf. A243753, A243827, A243828, A243829, A243830, A243832, A243833, A243834, A243835, A243836. %K A243831 nonn,tabl %O A243831 0,21 %A A243831 _Alois P. Heinz_, Jun 11 2014