|
%I #13 Jun 13 2015 00:54:16
%S 0,1,46,367,1805,7280,25781,83916,250062,676155,1662160,3748261,
%T 7839811,15370082,28505855,50400890,85502316,139914981,221828802,
%U 342014155,514390345,756672196,1091099801,1545256472,2152979930,2955371775,4001910276,5351671521
%N Number of 7-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 Alois P. Heinz, <a href="/A213286/b213286.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n) = n*(11954-29577*n+27640*n^2-12831*n^3+3234*n^4-420*n^5+24*n^6)/24.
%F G.f.: x*(1+38*x+27*x^2+101*x^3+610*x^4+693*x^5+3570*x^6)/(1-x)^8.
%e a(0) = 0: no word of length 7 is possible for an empty alphabet.
%e a(1) = 1: aaaaaaa for alphabet {a}.
%e a(2) = 46: aaaaaaa, aaaaaab, aaaaaba, aaaaabb, aaaabaa, aaaabab, aaaabba, aaaabbb, aaabaaa, aaabaab, aaababa, aaababb, aaabbaa, aaabbab, aaabbba, aabaaaa, aabaaab, aabaaba, aabaabb, aababaa, aababab, aababba, aabbaaa, aabbaab, aabbaba, abaaaaa, abaaaab, abaaaba, abaaabb, abaabaa, abaabab, abaabba, ababaaa, ababaab, abababa, baaaaaa, baaaaab, baaaaba, baaaabb, baaabaa, baaabab, baaabba, baabaaa, baabaab, baababa, bbbbbbb for alphabet {a,b}.
%p a:= n-> n*(11954+ (-29577 +(27640 +(-12831+(3234+(-420+24*n)*n) *n) *n) *n) *n)/24:
%p seq(a(n), n=0..40);
%Y Row n=7 of A213276.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jun 08 2012
|
