A162558 a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/6.

1, 6, 38, 248, 1644, 10984, 73672, 495072, 3329936, 22407776, 150819168, 1015220608, 6834184384, 46006990464, 309717848192, 2085024691712, 14036454256896, 94493999351296, 636137999861248, 4282512012883968

Offset

0,2

Comments

Fifth binomial transform of A108411. Binomial transform of A162557. Inverse binomial transform of A162757.

2nd binomial transform of A086405. - R. J. Mathar, Jul 17 2009

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (10, -22).

Formula

a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 1, a(1) = 6.

G.f.: (1-4*x)/(1-10*x+22*x^2).

From R. J. Mathar, Jul 17 2009: (Start)

a(n) = 10*a(n-2) - 22*a(n-2).

G.f.: (1-4*x)/(1-10*x+22*x^2). (End)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/6: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 13 2009

Crossrefs

Cf. A108411 (powers of 3 repeated), A162557, A162757.

Sequence in context: A180030 A135030 A217633 * A215466 A147957 A098410

Adjacent sequences: A162555 A162556 A162557 * A162559 A162560 A162561

Keyword

nonn

Author

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

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 13 2009

More terms from R. J. Mathar, Jul 17 2009

Status

approved