A277673 Number of n-length words over an n-ary alphabet {a_1,a_2,...,a_n} avoiding consecutive letters a_i, a_{i+1}.

1, 1, 3, 16, 136, 1547, 22012, 375231, 7445184, 168412696, 4275561136, 120338946469, 3718175865856, 125094920949797, 4551798150123456, 178094082550301368, 7455514741874966528, 332495821030327545527, 15737024371475868676864, 787813565550480151088691

Offset: 0

Author

Alois P. Heinz, Oct 26 2016

Keywords

• nonn

Examples

			a(3) = 16: 000, 002, 020, 021, 022, 100, 102, 110, 111, 200, 202, 210, 211, 220, 221, 222 (using ternary alphabet {0, 1, 2}).
		

Links

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

Crossrefs

Main diagonal of A277666.

Programs

Maple

b:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,
      -add((-1)^j*(k+1-j)*b(n-j, k), j=1..k)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

b[n_, k_] := b[n, k] = If[n < 0, 0, If[n == 0, 1,
     -Sum[(-1)^j (k+1-j) b[n-j, k], {j, 1, k}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 02 2021, after Alois P. Heinz *)

Formula

a(n) = [x^n] 1/(1+Sum_{j=1..n} (n+1-j)*(-x)^j).