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A213285 Number of 6-length words w over n-ary alphabet such that 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 A213285 #15 Jun 13 2015 00:54:16
%S A213285 0,1,27,165,712,2535,8151,23527,60600,140517,297595,584001,1075152,
%T A213285 1875835,3127047,5013555,7772176,11700777,17167995,24623677,34610040,
%U A213285 47773551,64877527,86815455,114625032,149502925,192820251,246138777,311227840,390081987,484939335
%N A213285 Number of 6-length words w over n-ary alphabet such that 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 A213285 Alois P. Heinz, <a href="/A213285/b213285.txt">Table of n, a(n) for n = 0..1000</a>
%H A213285 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A213285 a(n) = n*(-332+757*n-632*n^2+255*n^3-48*n^4+4*n^5)/4.
%F A213285 G.f.: x*(1+20*x-3*x^2+89*x^3+106*x^4+507*x^5) / (1-x)^7.
%e A213285 a(0) = 0: no word of length 6 is possible for an empty alphabet.
%e A213285 a(1) = 1: aaaaaa for alphabet {a}.
%e A213285 a(2) = 27: aaaaaa, aaaaab, aaaaba, aaaabb, aaabaa, aaabab, aaabba, aaabbb, aabaaa, aabaab, aababa, aababb, aabbaa, aabbab, abaaaa, abaaab, abaaba, abaabb, ababaa, ababab, baaaaa, baaaab, baaaba, baaabb, baabaa, baabab, bbbbbb for alphabet {a,b}.
%p A213285 a:= n-> n*(-332+(757+(-632+(255+(-48+4*n)*n)*n)*n)*n)/4:
%p A213285 seq(a(n), n=0..40);
%Y A213285 Row n=6 of A213276.
%K A213285 nonn,easy
%O A213285 0,3
%A A213285 _Alois P. Heinz_, Jun 08 2012