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 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. 13
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,21 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened EXAMPLE Square array A(n,k) begins:    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,  0,    0,    0,  0,    0,  0,   0, 0, 0,   0, ...    0,  0,    0,    0,  0,    0,  0,   0, 0, 0,   0, ...   42, 42,    1,    0,  0,    0,  0,   0, 0, 0,   0, ...    0,  0,   15,    1,  0,    1,  0,   0, 0, 0,   1, ...    0,  0,  105,   21,  0,    6,  0,   1, 0, 0,   1, ...    0,  0,  490,  196,  0,   42,  0,   8, 0, 0,  13, ...    0,  0, 1764, 1176,  0,  224,  0,  63, 0, 0,  52, ...    0,  0, 5292, 5292, 42, 1134, 42, 390, 0, 0, 244, ... CROSSREFS Main diagonal gives A243774 or column k=5 of A243752. Cf. A243753, A243827, A243828, A243829, A243830, A243832, A243833, A243834, A243835, A243836. Sequence in context: A237639 A095189 A023932 * A022074 A335188 A263303 Adjacent sequences:  A243828 A243829 A243830 * A243832 A243833 A243834 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jun 11 2014 STATUS approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)