A124191 a(n) = ((2 + 3*sqrt(2))^n - (2 - 3*sqrt(2))^n)/(2*sqrt(2)).

0, 3, 12, 90, 528, 3372, 20880, 130728, 815232, 5091120, 31777728, 198386592, 1238434560, 7731150528, 48262685952, 301286851200, 1880825008128, 11741315949312, 73296813911040, 457565678934528, 2856418110492672, 17831591947054080, 111316221335113728

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (4,14).

Formula

From Philippe Deléham, Dec 12 2006: (Start)

a(n) = 4*a(n-1) + 14*a(n-2) for n >= 2; a(0)=0, a(1)=3.

G.f.: 3x/(1-4*x-14*x^2). (End)

Mathematica

Expand[Table[((2 + 3Sqrt[2])^n - (2 - 3Sqrt[2])^n)/(2Sqrt[2]), {n, 0, 30}]]
LinearRecurrence[{4, 14}, {0, 3}, 50] (* Amiram Eldar, Mar 29 2020 *)

Crossrefs

Sequence in context: A367143 A361583 A361584 * A065087 A366733 A305870

Adjacent sequences: A124188 A124189 A124190 * A124192 A124193 A124194

Keyword

nonn,easy

Author

Artur Jasinski, Dec 10 2006

Extensions

More terms from Amiram Eldar, Mar 29 2020

Status

approved