A108146 a(n) = 4*a(n-1) - a(n-2) - a(n-3).

1, 1, 1, 2, 6, 21, 76, 277, 1011, 3691, 13476, 49202, 179641, 655886, 2394701, 8743277, 31922521, 116552106, 425542626, 1553695877, 5672688776, 20711516601, 75619681751, 276094521627, 1008046888156, 3680473349246, 13437751987201, 49062487711402, 179131725509161

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (4,-1,-1).

Formula

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

Mathematica

p = Expand[(x^3 - x^2 - x - 1)*(x^3 - 4*x^2 + x + 1)] v[0] = {1, 1, 1}; M = {{0, 1, 0}, {0, 0, 1}, {-1, -1, 4}}; Det[M - x*IdentityMatrix[3]] NSolve[Det[M - x*IdentityMatrix[3]] == 0, x] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 0, 50}]
LinearRecurrence[{4, -1, -1}, {1, 1, 1}, 29] (* Stefano Spezia, Dec 16 2025 *)

Crossrefs

Sequence in context: A294820 A116782 A112091 * A116798 A279560 A116821

Adjacent sequences: A108143 A108144 A108145 * A108147 A108148 A108149

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 05 2005

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

a(27)-a(28) from Stefano Spezia, Dec 16 2025

Status

approved