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 A321704 Number of words w of length n over an n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z. 1
 1, 1, 4, 18, 118, 895, 8151, 83916, 977026, 12602451, 178880725, 2766415036, 46314488705, 834067614601, 16074694453741, 330017679352180, 7188779521480810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = A213276(n,n). EXAMPLE a(3) = 18: aaa, aab, aac, aba, abc, aca, acb, baa, bac, bbb, bbc, bca, bcb, caa, cab, cba, cbb, ccc. MAPLE h:= proc(n, k, m, l) option remember; `if`(n=0 and k=0, b(l), `if`(k=0 or n>0 and n1 then for j from i+1 to nops(l) do if l[i]<=l[j] then return false elif l[j]>0 then break fi od fi; true end: a:= n-> h(n\$2, 0, []): seq(a(n), n=0..10); # Alois P. Heinz, Mar 29 2020 MATHEMATICA h[n_, k_, m_, l_] := h[n, k, m, l] = If[n == 0 && k === 0, b[l], If[k == 0 || n > 0 && n < m, 0, Sum[h[n - j, k - 1, Max[m, j], Join[{j}, l]], {j, Max[1, m], n}] + h[n, k - 1, m, Join[{0}, l]]]]; b[l_] := b[l] = If[Complement[l, {0}] == {}, 1, Sum[If[g[l, i], b[ReplacePart[l, i -> l[[i]] - 1]], 0], {i, 1, Length[l]}]]; g[l_, i_] := Module[{j}, If[l[[i]] < 1, Return[False], If[l[[i]] > 1, For[j = i + 1, j <= Length[l], j++, If[l[[i]] <= l[[j]], Return[False], If[l[[j]] > 0, Break[]]]]]]; True]; a[n_] := h[n, n, 0, {}]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 15}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz *) CROSSREFS Main diagonal of A213276. Sequence in context: A278994 A223008 A162224 * A296982 A222375 A053529 Adjacent sequences: A321701 A321702 A321703 * A321705 A321706 A321707 KEYWORD nonn,more AUTHOR Alois P. Heinz, Nov 17 2018 STATUS approved

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Last modified March 23 19:34 EDT 2023. Contains 361451 sequences. (Running on oeis4.)