A392274 Number of length n words over the alphabet [5] such that any prefix satisfies c(1) >= c(2), c(1) >= c(3), c(2) >= c(4), c(3) >= c(5), and c(4) >= c(5), where c(i) is the number of occurrences of the letter i.

1, 1, 3, 8, 23, 73, 246, 867, 3166, 11839, 45785, 179579, 717113, 2908753, 11954189, 49750400, 208980669, 885742796, 3787356399, 16314829868, 70763117954, 308802296807, 1355046242737, 5978469864061, 26504591207399, 118019589079173, 527734730588274, 2368700497250917

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

John Tyler Rascoe, Python code.

Example

All prefixes of the word [1, 3, 2, 4, 1, 5, 3] satisfy the required conditions so this word is counted under a(7) = 867.
a(3) = 8: [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 1], [1, 2, 3], [1, 2, 4], [1, 3, 1], [1, 3, 2].

Maple

b:= proc(n, l) option remember; `if`(n=0, 1, `if`(min(l[1], l[3])>0,
      b(n-1, map(x-> x-1, l)), 0)+add((h-> `if`(h[1]>h[2] or h[2]>h[4]
       or h[3]>h[4], 0, b(n-1, h)))(subsop(j=l[j]+1, l)), j=1..4))
    end:
a:= n-> b(n, [0$4]):
seq(a(n), n=0..27);  # Alois P. Heinz, Jan 10 2026

Mathematica

b[n_, l_] := b[n, l] = If[n == 0, 1, If[Min[l[[1]], l[[3]]] > 0,       b[n-1, l-1], 0] + Sum[Function[h, If[h[[1]] > h[[2]] || h[[2]] > h[[4]] || h[[3]] > h[[4]], 0, b[n-1, h]]][ReplacePart[l, j -> l[[j]]+1]], {j, 1, 4}]];
a[n_] := b[n, {0, 0, 0, 0}];
Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Apr 09 2026, after Alois P. Heinz *)

Prog

(Python) # see links

Crossrefs

Cf. A000351, A006966, A384725, A391270.

Sequence in context: A080410 A230952 A148777 * A124462 A047857 A101495

Adjacent sequences: A392271 A392272 A392273 * A392275 A392276 A392277

Keyword

nonn

Author

John Tyler Rascoe, Jan 05 2026

Extensions

a(15)-a(27) from Alois P. Heinz, Jan 10 2026

Status

approved