A277671 Number of n-length words over an 8-ary alphabet {a_1,a_2,...,a_8} avoiding consecutive letters a_i, a_{i+1}.

1, 8, 57, 406, 2892, 20600, 146736, 1045216, 7445184, 53032832, 377758463, 2690813426, 19166948203, 136528196220, 972504760052, 6927254109472, 49343562590512, 351479407373632, 2503624937520704, 17833584831080448, 127030508108889857, 904851724611169300

Offset: 0

Author

Alois P. Heinz, Oct 26 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-7,6,-5,4,-3,2,-1)

Crossrefs

Column k=8 of A277666.

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
      -add((-1)^j*(9-j)*a(n-j), j=1..8)))
    end:
seq(a(n), n=0..25);

Mathematica

LinearRecurrence[{8,-7,6,-5,4,-3,2,-1},{1,8,57,406,2892,20600,146736,1045216},30] (* Harvey P. Dale, May 15 2018 *)

Formula

G.f.: 1/(1 + Sum_{j=1..8} (9-j)*(-x)^j).