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A213283 Number of 4-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 A213283 #13 Jun 13 2015 00:54:15
%S A213283 0,1,9,36,118,315,711,1414,2556,4293,6805,10296,14994,21151,29043,
%T A213283 38970,51256,66249,84321,105868,131310,161091,195679,235566,281268,
%U A213283 333325,392301,458784,533386,616743,709515,812386,926064,1051281,1188793,1339380,1503846
%N A213283 Number of 4-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 A213283 Alois P. Heinz, <a href="/A213283/b213283.txt">Table of n, a(n) for n = 0..1000</a>
%H A213283 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A213283 a(n) = n*(-9+17*n-8*n^2+2*n^3)/2.
%F A213283 G.f.: x*(1+4*x+x^2+18*x^3)/(1-x)^5.
%e A213283 a(0) = 0: no word of length 4 is possible for an empty alphabet.
%e A213283 a(1) = 1: aaaa for alphabet {a}.
%e A213283 a(2) = 9: aaaa, aaab, aaba, aabb, abaa, abab, baaa, baab, bbbb for alphabet {a,b}.
%e A213283 a(3) = 36: aaaa, aaab, aaac, aaba, aabb, aabc, aaca, aacb, aacc, abaa, abab, abac, abca, acaa, acab, acac, acba, baaa, baab, baac, baca, bbbb, bbbc, bbcb, bbcc, bcaa, bcbb, bcbc, caaa, caab, caac, caba, cbaa, cbbb, cbbc, cccc for alphabet {a,b,c}.
%p A213283 a:= n-> n*(-9+(17+(-8+2*n)*n)*n)/2:
%p A213283 seq(a(n), n=0..40);
%Y A213283 Row n=4 of A213276.
%K A213283 nonn,easy
%O A213283 0,3
%A A213283 _Alois P. Heinz_, Jun 08 2012