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 A243827 Number A(n,k) of Dyck paths of semilength n having exactly one occurrence 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. 17
 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 4, 6, 1, 0, 0, 0, 0, 1, 2, 11, 10, 1, 0, 0, 0, 0, 0, 4, 6, 26, 15, 1, 0, 0, 0, 0, 0, 1, 11, 16, 57, 21, 1, 0, 0, 0, 0, 0, 1, 4, 26, 45, 120, 28, 1, 0, 0, 0, 0, 1, 1, 5, 15, 57, 126, 247, 36, 1, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,25 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, ...   1, 1, 1,  0,   0,    0,   0,    0,    0,    0, ...   0, 0, 1,  1,   1,    1,   1,    0,    0,    0, ...   0, 0, 1,  3,   4,    2,   4,    1,    1,    1, ...   0, 0, 1,  6,  11,    6,  11,    4,    5,    5, ...   0, 0, 1, 10,  26,   16,  26,   15,   21,   17, ...   0, 0, 1, 15,  57,   45,  57,   50,   78,   54, ...   0, 0, 1, 21, 120,  126, 120,  161,  274,  177, ...   0, 0, 1, 28, 247,  357, 247,  504,  927,  594, ...   0, 0, 1, 36, 502, 1016, 502, 1554, 3061, 1997, ... CROSSREFS Columns k=2-10 give: A000012(n) for n>0, A000217(n-1) for n>0, A000295(n-1) for n>0, A005717(n-1) for n>1, A000295(n-1) for n>0, A014532(n-2) for n>2, A108863, A244235, A244236. Main diagonal gives A243770 or column k=1 of A243752. Cf. A243753, A243828, A243829, A243830, A243831, A243832, A243833, A243834, A243835, A243836. Sequence in context: A255851 A078529 A180017 * A059530 A193525 A049828 Adjacent sequences:  A243824 A243825 A243826 * A243828 A243829 A243830 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jun 11 2014 STATUS approved

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Last modified October 20 16:03 EDT 2019. Contains 328267 sequences. (Running on oeis4.)