A321838 Number of words w of length n such that each letter of the binary alphabet is used at least once and 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.

2, 3, 7, 12, 25, 44, 89, 160, 321, 587, 1175, 2177, 4355, 8150, 16301, 30744, 61489, 116687, 233375, 445093, 890187, 1704793, 3409587, 6552377, 13104755, 25258599, 50517199, 97617059, 195234119, 378098954, 756197909, 1467343304, 2934686609, 5704370759

Offset: 2

Author

Alois P. Heinz, Nov 19 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..3327

Crossrefs

Column k=2 of A257783.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, [0, 2, 3][n],
      ((25*n^4-130*n^3-17*n^2+810*n-848)*a(n-1)
       +(2*(50*n^4-485*n^3+1596*n^2-2049*n+820))*a(n-2)
       -(4*(n-4))*(25*n^3-130*n^2+193*n-76)*a(n-3)
       )/((25*n^3-205*n^2+528*n-424)*(n+1)))
    end:
seq(a(n), n=2..40);

Formula

a(n) ~ 5 * 2^(n - 3/2) / sqrt(Pi*n). - Vaclav Kotesovec, Nov 21 2018