login
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.
2
0, 1, 27, 165, 712, 2535, 8151, 23527, 60600, 140517, 297595, 584001, 1075152, 1875835, 3127047, 5013555, 7772176, 11700777, 17167995, 24623677, 34610040, 47773551, 64877527, 86815455, 114625032, 149502925, 192820251, 246138777, 311227840, 390081987, 484939335
OFFSET
0,3
FORMULA
a(n) = n*(-332+757*n-632*n^2+255*n^3-48*n^4+4*n^5)/4.
G.f.: x*(1+20*x-3*x^2+89*x^3+106*x^4+507*x^5) / (1-x)^7.
EXAMPLE
a(0) = 0: no word of length 6 is possible for an empty alphabet.
a(1) = 1: aaaaaa for alphabet {a}.
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}.
MAPLE
a:= n-> n*(-332+(757+(-632+(255+(-48+4*n)*n)*n)*n)*n)/4:
seq(a(n), n=0..40);
CROSSREFS
Row n=6 of A213276.
Sequence in context: A042418 A042420 A372560 * A372444 A174617 A055339
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 08 2012
STATUS
approved