A147961 a(n) = ((6+sqrt(3))^n + (6-sqrt(3))^n)/2.

1, 6, 39, 270, 1953, 14526, 109863, 838998, 6442497, 49623030, 382873959, 2956927518, 22848289569, 176600866734, 1365216845031, 10554773538150, 81605126571777, 630953992102374, 4878478728359847, 37720263000939822

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-33).

Formula

From Philippe Deléham, Nov 19 2008: (Start)

a(n) = 12*a(n-1) - 33*a(n-2) for n > 1, with a(0)=1, a(1)=6.

G.f.: (1-6x)/(1-12x+33x^2).

a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2k)*3^(n-k))/6^n. (End)

Example

a(3)=270

Mathematica

CoefficientList[Series[(1-6x)/(1-12x+33x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, -33}, {1, 6}, 30] (* Harvey P. Dale, Jul 30 2021 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((6+r3)^n+(6-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008

Crossrefs

Sequence in context: A357206 A370026 A199491 * A264232 A068765 A349531

Adjacent sequences: A147958 A147959 A147960 * A147962 A147963 A147964

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008

Extensions

Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008

Status

approved