|
| |
|
|
A075155
|
|
Cubes of Lucas numbers.
|
|
5
| |
|
|
8, 1, 27, 64, 343, 1331, 5832, 24389, 103823, 438976, 1860867, 7880599, 33386248, 141420761, 599077107, 2537716544, 10749963743, 45537538411, 192900170952, 817138135549, 3461452853383, 14662949322176, 62113250509227
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| a(n)=3(-1)^n*L(n)+L(3n). Also a(n)=(-1)^n*A075151(n)
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,6,-3,-1).
|
|
|
FORMULA
| a(n) = (A000032(n))^3 = A000032(n) * A001254(n).
a(n)=L(n)*C(n)^2, L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084).
a(n)=3a(n-1)+6a(n-2)-3a(n-3)-a(n-4), n>=4.
G.f.: ( 8-23*x-24*x^2+x^3 ) / ( (x^2+4*x-1)*(x^2-x-1) ).
a(n) = 2*A001077(n) +3*A061084(n+1). - R. J. Mathar, Nov 17 2011
|
|
|
MAPLE
| CoefficientList[Series[(8-23*x-24*x^2+x^3)/(1-3*x-6*x^2+3*x^3+x^4), {x, 0, 25}], x].
|
|
|
PROG
| (MAGMA) [ Lucas(n)^3 : n in [0..120]]; // Vincenzo Librandi, Apr 14 2011
|
|
|
CROSSREFS
| Cf. A000032, A061084, A075150, A075151.
Third row of array A103324.
Sequence in context: A138505 A050458 A125166 * A075151 A028943 A050311
Adjacent sequences: A075152 A075153 A075154 * A075156 A075157 A075158
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Sep 06 2002
|
|
|
EXTENSIONS
| Simpler definition from Ralf Stephan, Nov 01 2004
|
| |
|
|
