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

2,1

Links

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

Formula

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

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);

Crossrefs

Column k=2 of A257783.

Sequence in context: A018240 A090596 A355385 * A298897 A054272 A259593

Adjacent sequences: A321835 A321836 A321837 * A321839 A321840 A321841

Keyword

nonn

Author

Alois P. Heinz, Nov 19 2018

Status

approved