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 A243830 #8 Jan 24 2019 17:14:32 %S A243830 0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,0,0,14,0,0,0,0,0,1,0,0,0,0,0,0,0, %T A243830 10,0,0,0,0,0,0,0,1,50,0,0,0,0,0,0,0,0,15,175,0,0,0,0,0,0,0,1,0,105, %U A243830 490,0,0,0,0,0,0,0,0,5,0,490,1176,0,0,0,0,0,0,0,0,0,30,14,1764,2520,0,0,0,0,0,0,0,0,1,0,140,210,5292,4950,0,0 %N A243830 Number A(n,k) of Dyck paths of semilength n having exactly four (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 A243830 Alois P. Heinz, <a href="/A243830/b243830.txt">Antidiagonals n = 0..140, flattened</a> %e A243830 Square array A(n,k) begins: %e A243830 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243830 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243830 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243830 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A243830 14, 14, 1, 0, 0, 0, 0, 0, 0, 0, ... %e A243830 0, 0, 10, 1, 0, 1, 0, 0, 0, 0, ... %e A243830 0, 0, 50, 15, 0, 5, 0, 1, 0, 0, ... %e A243830 0, 0, 175, 105, 0, 30, 0, 7, 0, 0, ... %e A243830 0, 0, 490, 490, 14, 140, 14, 48, 0, 0, ... %e A243830 0, 0, 1176, 1764, 210, 630, 210, 264, 0, 14, ... %Y A243830 Main diagonal gives A243773 or column k=4 of A243752. %Y A243830 Cf. A243753, A243827, A243828, A243829, A243831, A243832, A243833, A243834, A243835, A243836. %K A243830 nonn,tabl %O A243830 0,15 %A A243830 _Alois P. Heinz_, Jun 11 2014