|
Search: id:A105941
|
|
|
| A105941 |
|
Powers of Lucas numbers. |
|
+0
1
|
|
| 1, 3, 4, 7, 8, 9, 11, 16, 18, 27, 29, 32, 47, 49, 64, 76, 81, 121, 123, 199, 243, 256, 322, 324, 343, 521, 729, 841, 843, 1024, 1331, 1364, 2187, 2207, 2209, 2401, 3571, 4096, 5776, 5778, 5832, 6561, 9349, 14641, 15127, 15129, 16384, 16807, 19683, 24389
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 56.
Thomas Koshy, "Fibonacci and Lucas Numbers and Applications", Wiley, New York, 2001.
V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Lucas Number.
|
|
FORMULA
|
{a(n)} = {A000204) U {A001254) U 3rd powers U {A099923}U {A103325}... L(n)^2 = L(2n) + 2(-1)^n = L(n-1)*L(n+1) + 5(-1)^n. L(n)^3 = L(3n) + 3(-1)^n*L(n). L(n)^4 = L(4n) + 4(-1)^n*L(2n) + 6. L(n)^5 = L(5n) + 5(-1)^n*L(3n) + 10L(n).
|
|
CROSSREFS
|
A000032 Lucas numbers. A001254 Squares of Lucas numbers. A075155 Cubes of Lucas numbers. A099923 Fourth powers of Lucas numbers. A103325 Fifth powers of Lucas numbers. A103324 Square array T(n,k) read by antidiagonals: powers of Lucas numbers. A105317 Powers of Fibonacci numbers.
Cf. A000032, A001254, A075155, A099923, A103325, A103324, A105317.
Sequence in context: A075821 A120515 A047545 this_sequence A110133 A100452 A004201
Adjacent sequences: A105938 A105939 A105940 this_sequence A105942 A105943 A105944
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 27 2005
|
|
|
Search completed in 0.002 seconds
|
