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