|
|
A242631
|
|
Number of n-length words w over an 8-ary alphabet {a_1,...,a_8} such that w contains never more than j consecutive letters a_j (for 1<=j<=8).
|
|
2
|
|
|
1, 8, 63, 496, 3904, 30729, 241871, 1903792, 14984945, 117948062, 928381475, 7307387240, 57517205708, 452723914009, 3563437058402, 28048184061555, 220770176730345, 1737705044525640, 13677657310833723, 107658264618591797, 847389408675004032, 6669890253930098674
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -(x^2+x+1) *(x^6+x^3+1) *(x+1) *(x^2+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) *(x^4+x^3+x^2+x+1) / (7*x^27 +20*x^26 +46*x^25 +90*x^24 +159*x^23 +249*x^22 +369*x^21 +507*x^20 +659*x^19 +809*x^18 +950*x^17 +1056*x^16 +1128*x^15 +1148*x^14 +1119*x^13 +1039*x^12 +927*x^11 +782*x^10 +631*x^9 +480*x^8 +345*x^7 +229*x^6 +144*x^5 +79*x^4 +39*x^3 +16*x^2 +5*x-1).
|
|
MAPLE
|
b:= proc(n, k, c, t) option remember;
`if`(n=0, 1, add(`if`(c=t and j=c, 0,
b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))
end:
a:= n-> b(n, 8, 0$2):
seq(a(n), n=0..30);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|