A121401 a(n) = ((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).

2, 3, 8, 27, 98, 363, 1352, 5043, 18818, 70227, 262088, 978123, 3650402, 13623483, 50843528, 189750627, 708158978, 2642885283, 9863382152, 36810643323, 137379191138, 512706121227, 1913445293768, 7141075053843, 26650854921602

Offset

0,1

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

Formula

a(n) = ((2+sqrt(3))^n+(2-sqrt(3))^n)/2.

a(n) = A001075(n)+1.

From R. J. Mathar, Aug 07 2008: (Start)

a(n) = A102206(n-1).

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

a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3). - Wesley Ivan Hurt, Jan 16 2024

Mathematica

Table[((-1+Sqrt[3])^n+(1+Sqrt[3])^n)^2/(2^(n+1)), {n, 0, 25}]
LinearRecurrence[{5, -5, 1}, {2, 3, 8}, 25] (* Ray Chandler, Jan 27 2014 *)

Crossrefs

Cf. A001075, A102206.

Sequence in context: A183948 A041503 A086613 * A318895 A093858 A080568

Adjacent sequences: A121398 A121399 A121400 * A121402 A121403 A121404

Keyword

nonn,easy

Author

Zak Seidov, Sep 06 2006

Status

approved