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 A264909 Number A(n,k) of k-ascent sequences of length n with no consecutive repeated letters; square array A(n,k), n>=0, k>=0, read by antidiagonals. 12
 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 3, 6, 5, 0, 1, 1, 4, 12, 21, 16, 0, 1, 1, 5, 20, 54, 87, 61, 0, 1, 1, 6, 30, 110, 276, 413, 271, 0, 1, 1, 7, 42, 195, 670, 1574, 2213, 1372, 0, 1, 1, 8, 56, 315, 1380, 4470, 9916, 13205, 7795, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened S. Kitaev, J. Remmel, p-Ascent Sequences, arXiv:1503.00914 [math.CO], 2015. EXAMPLE Square array A(n,k) begins:   1,   1,    1,    1,     1,     1,      1,      1, ...   1,   1,    1,    1,     1,     1,      1,      1, ...   0,   1,    2,    3,     4,     5,      6,      7, ...   0,   2,    6,   12,    20,    30,     42,     56, ...   0,   5,   21,   54,   110,   195,    315,    476, ...   0,  16,   87,  276,   670,  1380,   2541,   4312, ...   0,  61,  413, 1574,  4470, 10555,  21931,  41468, ...   0, 271, 2213, 9916, 32440, 86815, 201761, 422128, ... MAPLE b:= proc(n, k, i, t) option remember; `if`(n<1, 1, add(       `if`(j=i, 0, b(n-1, k, j, t+`if`(j>i, 1, 0))), j=0..t+k))     end: A:= (n, k)-> b(n-1, k, 0\$2): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA b[n_, k_, i_, t_] := b[n, k, i, t] = If[n<1, 1, Sum[If[j == i, 0, b[n-1, k, j, t + If[j>i, 1, 0]]], {j, 0, t+k}]]; A[n_, k_] := b[n-1, k, 0, 0]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Feb 17 2016, after Alois P. Heinz *) CROSSREFS Columns k=1-10 give: A138265, A263852, A263853, A263854, A264910, A264911, A264912, A264913, A264914, A264915. Rows k=0+1,2-4 give: A000012, A001477, A002378, A160378(n+1). Main diagonal gives A264916. Sequence in context: A112555 A108561 A174626 * A104579 A079531 A182882 Adjacent sequences:  A264906 A264907 A264908 * A264910 A264911 A264912 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Nov 28 2015 STATUS approved

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Last modified October 19 14:50 EDT 2019. Contains 328223 sequences. (Running on oeis4.)