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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
OFFSET
0,2
LINKS
Geoffrey Critzer and Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, 16, 39, 79, 144, 229, 345, 480, 631, 782, 927, 1039, 1119, 1148, 1128, 1056, 950, 809, 659, 507, 369, 249, 159, 90, 46, 20, 7).
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
Column k=8 of A242464.
Sequence in context: A370038 A081107 A164592 * A001090 A243782 A369810
KEYWORD
nonn,easy
AUTHOR
STATUS
approved