|
| |
|
|
A099923
|
|
Fourth powers of Lucas numbers A000032.
|
|
5
| |
|
|
16, 1, 81, 256, 2401, 14641, 104976, 707281, 4879681, 33362176, 228886641, 1568239201, 10750371856, 73680216481, 505022001201, 3461445366016, 23725169980801, 162614549665681, 1114577187760656, 7639424429247601
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 56.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,15,-15,-5,1).
|
|
|
FORMULA
| a(n) = (A000032(n))^4 = (A001254(n))^2.
L(4n) + 4(-1)^n*L(2n) + 6.
For n>1, L(n-2)*L(n-1)*L(n+1)*L(n+2) + 25.
G.f.: (16-79x-164x^2+76x^3+x^4)/((1-x)(1+3x+x^2)(1-7x+x^2)). [T. Mansour, Australas. J. Combin. 30 (2004), 207] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2008]
|
|
|
PROG
| (MAGMA) [ Lucas(n)^4 : n in [0..120]]; // Vincenzo Librandi, Apr 14 2011
|
|
|
CROSSREFS
| Cf. A075515.
Fourth row of array A103324.
Sequence in context: A097522 A040271 A036179 * A105671 A145828 A095876
Adjacent sequences: A099920 A099921 A099922 * A099924 A099925 A099926
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Ralf Stephan, Nov 01 2004
|
| |
|
|
