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A213283 Number of 4-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, 9, 36, 118, 315, 711, 1414, 2556, 4293, 6805, 10296, 14994, 21151, 29043, 38970, 51256, 66249, 84321, 105868, 131310, 161091, 195679, 235566, 281268, 333325, 392301, 458784, 533386, 616743, 709515, 812386, 926064, 1051281, 1188793, 1339380, 1503846 (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 (5,-10,10,-5,1).

FORMULA

a(n) = n*(-9+17*n-8*n^2+2*n^3)/2.

G.f.: x*(1+4*x+x^2+18*x^3)/(1-x)^5.

EXAMPLE

a(0) = 0: no word of length 4 is possible for an empty alphabet.

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

a(2) = 9: aaaa, aaab, aaba, aabb, abaa, abab, baaa, baab, bbbb for alphabet {a,b}.

a(3) = 36: aaaa, aaab, aaac, aaba, aabb, aabc, aaca, aacb, aacc, abaa, abab, abac, abca, acaa, acab, acac, acba, baaa, baab, baac, baca, bbbb, bbbc, bbcb, bbcc, bcaa, bcbb, bcbc, caaa, caab, caac, caba, cbaa, cbbb, cbbc, cccc for alphabet {a,b,c}.

MAPLE

a:= n-> n*(-9+(17+(-8+2*n)*n)*n)/2:

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

CROSSREFS

Row n=4 of A213276.

Sequence in context: A193007 A259279 A168569 * A188162 A023872 A034557

Adjacent sequences:  A213280 A213281 A213282 * A213284 A213285 A213286

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 08 2012

STATUS

approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)