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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. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

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: A224001 A042418 A042420 * A174617 A055339 A269054

Adjacent sequences:  A213282 A213283 A213284 * A213286 A213287 A213288

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 08 2012

STATUS

approved

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Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)