cp's OEIS Frontend

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.

%I A321838 #7 Nov 21 2018 11:31:28
%S A321838 2,3,7,12,25,44,89,160,321,587,1175,2177,4355,8150,16301,30744,61489,
%T A321838 116687,233375,445093,890187,1704793,3409587,6552377,13104755,
%U A321838 25258599,50517199,97617059,195234119,378098954,756197909,1467343304,2934686609,5704370759
%N 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.
%H A321838 Alois P. Heinz, <a href="/A321838/b321838.txt">Table of n, a(n) for n = 2..3327</a>
%F A321838 a(n) ~ 5 * 2^(n - 3/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Nov 21 2018
%p A321838 a:= proc(n) option remember; `if`(n<4, [0, 2, 3][n],
%p A321838       ((25*n^4-130*n^3-17*n^2+810*n-848)*a(n-1)
%p A321838        +(2*(50*n^4-485*n^3+1596*n^2-2049*n+820))*a(n-2)
%p A321838        -(4*(n-4))*(25*n^3-130*n^2+193*n-76)*a(n-3)
%p A321838        )/((25*n^3-205*n^2+528*n-424)*(n+1)))
%p A321838     end:
%p A321838 seq(a(n), n=2..40);
%Y A321838 Column k=2 of A257783.
%K A321838 nonn
%O A321838 2,1
%A A321838 _Alois P. Heinz_, Nov 19 2018