A277672 Number of n-length words over a 9-ary alphabet {a_1,a_2,...,a_9} avoiding consecutive letters a_i, a_{i+1}.

1, 9, 73, 592, 4801, 38935, 315754, 2560693, 20766637, 168412696, 1365788605, 11076234500, 89825738954, 728466283251, 5907695633935, 47910065991605, 388539722685585, 3150968653039294, 25553638078006016, 207234184444162395, 1680622033979603605

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 (9,-8,7,-6,5,-4,3,-2,1)

Crossrefs

Column k=9 of A277666.

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
      -add((-1)^j*(10-j)*a(n-j), j=1..9)))
    end:
seq(a(n), n=0..25);

Mathematica

LinearRecurrence[{9,-8,7,-6,5,-4,3,-2,1},{1,9,73,592,4801,38935,315754,2560693,20766637},30] (* Harvey P. Dale, Apr 03 2019 *)

Formula

G.f.: 1/(1 + Sum_{j=1..9} (10-j)*(-x)^j).