A242635 Number of n-length words w over an n-ary alphabet {a_1,...,a_n} such that w contains never more than j consecutive letters a_j for 1<=j<=n.

1, 1, 3, 21, 208, 2631, 40295, 724892, 14984945, 350068993, 9121438862, 262285777567, 8250643190038, 281849526767134, 10390959086757005, 411219228179234026, 17387847546353549435, 782342249208357483984, 37321230268969840324231, 1881590248383756833279387

Offset: 0

Author

Geoffrey Critzer and Alois P. Heinz, May 19 2014

Keywords

• nonn

Links

• Geoffrey Critzer and Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Main diagonal of A242464.

Programs

Maple

a:= proc(n) option remember; local v;
      v:= i-> (x-x^(i+1))/(1-x);
      coeff(series(1/(1-add(v(i)/(1+v(i)), i=1..n)), x, n+1), x, n)
    end:
seq(a(n), n=0..25);

Mathematica

b[n_, k_, c_, t_] := b[n, k, c, t] = If[n == 0, 1, Sum[If[c == t && j == c, 0, b[n - 1, k, j, 1 + If[j == c, t, 0]]], {j, 1, k}]];
a[n_] := b[n, n, 0, 0];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 28 2020, from Maple code of A242464 *)

Formula

a(n) = [x^n] 1/(1-Sum_{i=1..n} v(i)/(1+v(i))) with v(i) = (x-x^(i+1))/(1-x).

a(n) ~ n^n. - Vaclav Kotesovec, Aug 27 2014