A213284 Number of 5-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.

0, 1, 14, 74, 276, 895, 2506, 6104, 13224, 26061, 47590, 81686, 133244, 208299, 314146, 459460, 654416, 910809, 1242174, 1663906, 2193380, 2850071, 3655674, 4634224, 5812216, 7218725, 8885526, 10847214, 13141324, 15808451, 18892370, 22440156, 26502304

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 (6,-15,20,-15,6,-1).

Formula

a(n) = n*(94-204*n+155*n^2-45*n^3+6*n^4)/6.

G.f.: x*(1+8*x+5*x^2+22*x^3+84*x^4)/(1-x)^6.

Example

a(0) = 0: no word of length 5 is possible for an empty alphabet.
a(1) = 1: aaaaa for alphabet {a}.
a(2) = 14: aaaaa, aaaab, aaaba, aaabb, aabaa, aabab, aabba, abaaa, abaab, ababa, baaaa, baaab, baaba, bbbbb for alphabet {a,b}.

Maple

a:= n-> n*(94+(-204+(155+(-45+6*n)*n)*n)*n)/6:
seq(a(n), n=0..40);

Crossrefs

Row n=5 of A213276.

Sequence in context: A279447 A205590 A369244 * A232377 A146563 A205583

Adjacent sequences: A213281 A213282 A213283 * A213285 A213286 A213287

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 08 2012

Status

approved