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A213287 Number of 8-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, 91, 869, 4895, 21562, 83728, 296268, 977026, 2990967, 8418649, 21740455, 51758345, 114517208, 237528214, 465636886, 868918932, 1553027197, 2672453415, 4447208761, 7183467523, 11298758534, 17352329324, 26081348272, 38443650358, 55667772435, 79311064261 (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 (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(n) = n*(-417562 +1092135*n -1113650*n^2 +587165*n^3 -175728*n^4 +30520*n^5 -2880*n^6 +120*n^7)/120.

G.f.: x*(1+82*x +86*x^2 +266*x^3 +1273*x^4 +4234*x^5 +5880*x^6 +28498*x^7) / (1-x)^9.

EXAMPLE

a(0) = 0: no word of length 8 is possible for an empty alphabet.

a(1) = 1: aaaaaaaa for alphabet {a}.

a(2) = 91: aaaaaaaa, aaaaaaab, ..., baababab, bbbbbbbb for alphabet {a,b}.

MAPLE

a:= n-> n*(-417562+ (1092135+ (-1113650+ (587165+ (-175728+ (30520+ (-2880+120*n) *n) *n) *n) *n) *n) *n)/120:

seq(a(n), n=0..40);

CROSSREFS

Row n=8 of A213276.

Sequence in context: A047696 A043459 A038488 * A072393 A085952 A129255

Adjacent sequences:  A213284 A213285 A213286 * A213288 A213289 A213290

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 08 2012

STATUS

approved

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Last modified December 16 04:19 EST 2018. Contains 318158 sequences. (Running on oeis4.)