A162560 a(n) = (4+sqrt(3))*(3+sqrt(3))^n + (4-sqrt(3))*(3-sqrt(3))^n.

3, 8, 30, 132, 612, 2880, 13608, 64368, 304560, 1441152, 6819552, 32270400, 152705088, 722608128, 3419418240, 16180860672, 76568654592, 362326763520, 1714548653568, 8113331340288, 38392696120320, 181676188680192

Offset

-1,1

Comments

Equals b(k) = ((9+sqrt(3))*(3-sqrt(3))^k+(9-sqrt(3))*(3+sqrt(3))^k)/6 for k >= 0. - Klaus Brockhaus, Jul 14 2009

Third binomial transform of A162852.

Links

Table of n, a(n) for n=-1..20.

Index entries for linear recurrences with constant coefficients, signature (6,-6).

Formula

a(n) = 6*a(n-1) - 6*a(n-2) for n > 0; a(-1) = 3, a(0) = 8.

G.f.: (3-10*x)/(x*(1-6*x+6*x^2)).

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(3+r)^n+(4-r)*(3-r)^n): n in [-1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009

Crossrefs

Cf. A162852 (3, -1, 9, -3, 27, -9, 81, ...).

Sequence in context: A360991 A361135 A348662 * A293250 A096161 A161779

Adjacent sequences: A162557 A162558 A162559 * A162561 A162562 A162563

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

Extensions

Edited and extended beyond a(5)=13608 by Klaus Brockhaus, Jul 18 2009

Status

approved