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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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 08 2012
STATUS
approved

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Last modified March 4 15:47 EST 2024. Contains 370532 sequences. (Running on oeis4.)