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A121401
a(n) = ((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).
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
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
Sequence in context: A183948 A041503 A086613 * A318895 A093858 A080568
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Sep 06 2006
STATUS
approved