A277667 Number of n-length words over a quaternary alphabet {a_1,a_2,...,a_4} avoiding consecutive letters a_i, a_{i+1}.

1, 4, 13, 42, 136, 440, 1423, 4602, 14883, 48132, 155660, 503408, 1628033, 5265096, 17027441, 55067134, 178088372, 575941872, 1862609199, 6023720790, 19480850935, 63001517896, 203748351160, 658926832032, 2130984459505, 6891652526348, 22287762039781

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 (4,-3,2,-1)

Formula

G.f.: 1/(1 + Sum_{j=1..4} (5-j)*(-x)^j).

Example

a(3) = 42: 000, 002, 003, 020, 021, 022, 030, 031, 032, 033, 100, 102, 103, 110, 111, 113, 130, 131, 132, 133, 200, 202, 203, 210, 211, 213, 220, 221, 222, 300, 302, 303, 310, 311, 313, 320, 321, 322, 330, 331, 332, 333 (using alphabet {0, 1, 2, 3}).

Maple

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

Crossrefs

Column k=4 of A277666.

Sequence in context: A289807 A022029 A010919 * A274952 A010900 A175005

Adjacent sequences: A277664 A277665 A277666 * A277668 A277669 A277670

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 26 2016

Status

approved