A277668 Number of n-length words over a 5-ary alphabet {a_1,a_2,...,a_5} avoiding consecutive letters a_i, a_{i+1}.

1, 5, 21, 88, 369, 1547, 6486, 27194, 114017, 478042, 2004299, 8403476, 35233470, 147724276, 619367372, 2596837513, 10887827441, 45649674187, 191396563242, 802473294131, 3364550422879, 14106637106664, 59145260271900, 247979854176461, 1039711513563070

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4,3,-2,1)

Formula

G.f.: 1/(1 + Sum_{j=1..5} (6-j)*(-x)^j).

Maple

a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,
          <0|0|0|0|1>, <1|-2|3|-4|5>>^n)[5, 5]:
seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{5, -4, 3, -2, 1}, {1, 5, 21, 88, 369}, 30] (* Harvey P. Dale, Oct 08 2017 *)

Crossrefs

Column k=5 of A277666.

Cf. A284840.

Sequence in context: A010925 A019992 A010917 * A270494 A347041 A267268

Adjacent sequences: A277665 A277666 A277667 * A277669 A277670 A277671

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 26 2016

Status

approved