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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)