A242635 - OEIS

%I #17 Dec 28 2020 04:23:36

%S 1,1,3,21,208,2631,40295,724892,14984945,350068993,9121438862,

%T 262285777567,8250643190038,281849526767134,10390959086757005,

%U 411219228179234026,17387847546353549435,782342249208357483984,37321230268969840324231,1881590248383756833279387

%N 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.

%H Geoffrey Critzer and Alois P. Heinz, <a href="/A242635/b242635.txt">Table of n, a(n) for n = 0..386</a>

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

%F a(n) ~ n^n. - _Vaclav Kotesovec_, Aug 27 2014

%p a:= proc(n) option remember; local v;

%p       v:= i-> (x-x^(i+1))/(1-x);

%p       coeff(series(1/(1-add(v(i)/(1+v(i)), i=1..n)), x, n+1), x, n)

%p     end:

%p seq(a(n), n=0..25);

%t 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}]];

%t a[n_] := b[n, n, 0, 0];

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Dec 28 2020, from Maple code of A242464 *)

%Y Main diagonal of A242464.

%K nonn

%O 0,3

%A _Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014