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 A240608 Number A(n,k) of n-length words w over a k-ary alphabet such that w is empty or a prefix z concatenated with letter a_i and i=1 or 0 < #(z,a_{i-1}) >= #(z,a_i), where #(z,a_i) counts the occurrences of the i-th letter in z; square array A(n,k), n>=0, k>=0, read by antidiagonals. 11
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 4, 1, 0, 1, 1, 2, 5, 7, 1, 0, 1, 1, 2, 5, 13, 14, 1, 0, 1, 1, 2, 5, 14, 35, 25, 1, 0, 1, 1, 2, 5, 14, 45, 94, 50, 1, 0, 1, 1, 2, 5, 14, 46, 149, 254, 91, 1, 0, 1, 1, 2, 5, 14, 46, 164, 509, 688, 182, 1, 0, 1, 1, 2, 5, 14, 46, 165, 629, 1756, 1872, 336, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Alois P. Heinz, Antidiagonals n = 0..36, flattened EXAMPLE Square array A(n,k) begins:   1, 1,  1,   1,    1,    1,    1,    1,    1, ...   0, 1,  1,   1,    1,    1,    1,    1,    1, ...   0, 1,  2,   2,    2,    2,    2,    2,    2, ...   0, 1,  4,   5,    5,    5,    5,    5,    5, ...   0, 1,  7,  13,   14,   14,   14,   14,   14, ...   0, 1, 14,  35,   45,   46,   46,   46,   46, ...   0, 1, 25,  94,  149,  164,  165,  165,  165, ...   0, 1, 50, 254,  509,  629,  650,  651,  651, ...   0, 1, 91, 688, 1756, 2511, 2742, 2770, 2771, ... MAPLE b:= proc(n, k, l) option remember; `if`(n=0, 1, `if`(nops(l) b(n, min(k, n), []): seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA b[n_, k_, l_List] := b[n, k, l] = If[n == 0, 1, If[Length[l] l[[i]]+1]], 0], {i, 1, Length[l]}]]; A[n_, k_] := b[n, Min[k, n], {}]; Table[ Table[A[n, d-n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Jan 19 2015, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000007, A000012, A026010(n-1) for n>0, A240609, A240610, A240611, A240612, A240613, A240614, A240615, A240616. Main diagonal gives A240617. Cf. A182172. Sequence in context: A182458 A238093 A238095 * A080934 A320955 A288942 Adjacent sequences:  A240605 A240606 A240607 * A240609 A240610 A240611 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Apr 09 2014 STATUS approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)