A373554 Number of ternary length-2 squarefree words of length n not containing the subwords 021 or 10.

1, 3, 5, 7, 11, 16, 24, 36, 53, 80, 118, 177, 263, 392, 585, 870, 1299, 1933, 2883, 4295, 6400, 9540, 14212, 21185, 31564, 47042, 70101, 104463, 155680, 231985, 345722, 515187, 767749, 1144111, 1704963, 2540784, 3786288, 5642420, 8408397

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1).

Formula

a(n) = 2*a(n-2) + a(n-3) - a(n-4).

G.f.: ((1+x)*(1+2*x+x^2-x^3))/(1-2*x^2-x^3+x^4).

Example

For n=3 the a(3)=7 solutions are  012, 020, 120, 121, 201, 202, 212.

Mathematica

LinearRecurrence[{0, 2, 1, -1}, {1, 3, 5, 7, 11}, 50] (* Paolo Xausa, Jan 19 2026 *)

Crossrefs

Sequence in context: A116582 A052003 A019449 * A219533 A094615 A245396

Adjacent sequences: A373551 A373552 A373553 * A373555 A373556 A373557

Keyword

nonn,easy

Author

Miquel A. Fiol, Jun 09 2024

Status

approved