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A213288 Number of 9-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 A213288 #13 Jun 13 2015 00:54:16
%S A213288 0,1,162,2074,13280,64924,273248,1050777,3754472,12602451,39598078,
%T A213288 115470300,311272072,777274550,1808153452,3946185587,8137258032,
%U A213288 15957939797,29935676058,53988338158,94013898576,158665898944,260355640952,416527654621,651260985944
%N A213288 Number of 9-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 A213288 Alois P. Heinz, <a href="/A213288/b213288.txt">Table of n, a(n) for n = 0..1000</a>
%H A213288 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A213288 a(n) = n*(3353416 -9177198*n +10002755*n^2 -5796570*n^3 +1984509*n^4 -416052*n^5 +52920*n^6 -3780*n^7 +120*n^8)/120.
%F A213288 G.f.: x*(1+152*x +499*x^2 -290*x^3 +6224*x^4 +6496*x^5 +41203*x^6 +52034*x^7 +256561*x^8) / (1-x)^10.
%e A213288 a(0) = 0: no word of length 9 is possible for an empty alphabet.
%e A213288 a(1) = 1: aaaaaaaaa for alphabet {a}.
%e A213288 a(2) = 162: aaaaaaaaa, aaaaaaaab, ..., baabababa, bbbbbbbbb for alphabet {a,b}.
%p A213288 a:= n-> n*(3353416+ (-9177198+ (10002755+ (-5796570+ (1984509+ (-416052+ (52920+ (-3780+120*n) *n) *n) *n) *n) *n) *n) *n)/120:
%p A213288 seq(a(n), n=0..40);
%Y A213288 Row n=9 of A213276.
%K A213288 nonn,easy
%O A213288 0,3
%A A213288 _Alois P. Heinz_, Jun 08 2012