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 A243833 #8 Feb 03 2019 07:37:17 %S A243833 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A243833 0,429,0,0,0,0,0,0,0,429,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,28,0,0, %U A243833 0,0,0,0,0,0,0,0,1,336,0,0,0,0,0,0,0,0,0,0,0,36,2520,0,0,0,0,0,0,0,0,0,0,1,0,540,13860,0,0 %N A243833 Number A(n,k) of Dyck paths of semilength n having exactly seven (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 A243833 Alois P. Heinz, <a href="/A243833/b243833.txt">Antidiagonals n = 0..140, flattened</a> %e A243833 Square array A(n,k) begins: %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 429, 429, 1, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243833 0, 0, 28, 1, 0, 1, 0, 0, 0, 0, 1, ... %e A243833 0, 0, 336, 36, 0, 8, 0, 1, 0, 0, 1, ... %e A243833 0, 0, 2520, 540, 0, 72, 0, 10, 0, 0, 17, ... %Y A243833 Main diagonal gives A243776 or column k=7 of A243752. %Y A243833 Cf. A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243834, A243835, A243836. %K A243833 nonn,tabl %O A243833 0,36 %A A243833 _Alois P. Heinz_, Jun 11 2014