A125817 a(n) = ((1 + 3*sqrt(2))^n - (1 - 3*sqrt(2))^n)/(2*sqrt(2)).

0, 3, 6, 63, 228, 1527, 6930, 39819, 197448, 1071819, 5500254, 29221431, 151947180, 800658687, 4184419434, 21980036547, 115095203472, 603851028243, 3164320515510, 16594108511151, 86981665785972, 456063176261511, 2390814670884546, 12534703338214779

Offset: 0

Author

Artur Jasinski, Dec 10 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from T. D. Noe)
• Index entries for linear recurrences with constant coefficients, signature (2, 17).

Programs

GAP

a:=[0,3];; for n in [3..30] do a[n]:=2*a[n-1]+17*a[n-2]; od; a; # G. C. Greubel, Aug 02 2019

Magma

I:=[0,3]; [n le 2 select I[n] else 2*Self(n-1) +17*Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 02 2019

Mathematica

Expand[Table[((1+3Sqrt[2])^n -(1-3Sqrt[2])^n)/(2Sqrt[2]), {n, 0, 30}]]
LinearRecurrence[{2, 17}, {0, 3}, 30] (* T. D. Noe, Mar 28 2012 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(3*x/(1-2*x-17*x^2))) \\ G. C. Greubel, Aug 02 2019

Sage

(3*x/(1-2*x-17*x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 02 2019

Formula

From Philippe Deléham, Dec 12 2006: (Start)

a(n) = 2*a(n-1) + 17*a(n-2), with a(0)=0, a(1)=3.

G.f.: 3*x/(1-2*x-17*x^2). (End)