A242632 Number of n-length words w over a 9-ary alphabet {a_1,...,a_9} such that w contains never more than j consecutive letters a_j (for 1<=j<=9).

1, 9, 80, 711, 6318, 56143, 498896, 4433274, 39394819, 350068993, 3110771999, 27642843622, 245638961566, 2182789161071, 19396631915857, 172361736254288, 1531635402139359, 13610370004776711, 120944038906506659, 1074729088326395697, 9550223588843166996

Offset

0,2

Links

Geoffrey Critzer and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(x+1) *(x^4-x^3+x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+x+1) *(x^6+x^3+1) *(x^2+1)*(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) / (8*x^31 +15*x^30 +38*x^29 +66*x^28 +118*x^27 +179*x^26 +273*x^25 +371*x^24 +503*x^23 +628*x^22 +775*x^21 +895*x^20 +1023*x^19 +1099*x^18 +1167*x^17 +1172*x^16 +1161*x^15 +1087*x^14 +1007*x^13 +875*x^12 +754*x^11 +606*x^10 +483*x^9 +352*x^8 +258*x^7 +166*x^6 +109*x^5 +59*x^4 +34*x^3 +12*x^2 +7*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, 9, 0$2):
seq(a(n), n=0..30);

Crossrefs

Column k=9 of A242464.

Sequence in context: A370039 A081108 A176174 * A018913 A359921 A192214

Adjacent sequences: A242629 A242630 A242631 * A242633 A242634 A242635

Keyword

nonn,easy

Author

Geoffrey Critzer and Alois P. Heinz, May 19 2014

Status

approved