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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
OFFSET
2,1
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 19 2018
STATUS
approved