A242629 Number of n-length words w over a 6-ary alphabet {a_1,...,a_6} such that w contains never more than j consecutive letters a_j (for 1<=j<=6).

1, 6, 35, 204, 1188, 6919, 40295, 234672, 1366694, 7959418, 46354440, 269961210, 1572213035, 9156329637, 53325071447, 310557107219, 1808637367513, 10533228997581, 61343923944270, 357257684774972, 2080614429665859, 12117182049311250, 70568625653399251

Offset

0,2

Links

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

Formula

G.f.: -(x^6+x^5+x^4+x^3+x^2+x+1) *(x+1)*(x^2-x+1) *(x^2+x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) / (5*x^17 +14*x^16 +32*x^15 +57*x^14 +90*x^13 +123*x^12 +155*x^11 +174*x^10 +181*x^9 +170*x^8 +148*x^7 +114*x^6 +81*x^5 +49*x^4 +26*x^3 +10*x^2 +3*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, 6, 0$2):
seq(a(n), n=0..30);

Crossrefs

Column k=6 of A242464.

Sequence in context: A289784 A161727 A121838 * A001109 A352972 A180033

Adjacent sequences: A242626 A242627 A242628 * A242630 A242631 A242632

Keyword

nonn,easy

Author

Geoffrey Critzer and Alois P. Heinz, May 19 2014

Status

approved