|
Search: id:A085480
|
|
|
| A085480 |
|
a(n) = p^n + q^n, where p = (3 + sqrt 21)/2, q = (3 - sqrt 21)/2. |
|
+0
2
|
|
| 3, 15, 54, 207, 783, 2970, 11259, 42687, 161838, 613575, 2326239, 8819442, 33437043, 126769455, 480619494, 1822166847, 6908359023, 26191577610, 99299809899, 376474162527, 1427321917278, 5411388239415, 20516130470079
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
A Jacobsthal variation.
p - q = sqrt 21; pq = -3; p + q = 3.
|
|
REFERENCES
|
Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
|
|
LINKS
|
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
|
|
FORMULA
|
a(n)=3*a(n-1)+3*a(n-2), a(1)=3, a(2)=15. G.f.: 3x*(1+2x)/(1-3x-3x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
|
|
EXAMPLE
|
a(4) = q^4 + q^4 = 207; p^5 + q^5 = 783, where p = (3 + sqrt 21)/2, q = (3 - sqrt 21)/2.
|
|
CROSSREFS
|
Cf. A030195.
Sequence in context: A166035 A038192 A147618 this_sequence A099581 A026696 A082708
Adjacent sequences: A085477 A085478 A085479 this_sequence A085481 A085482 A085483
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 02 2003
|
|
EXTENSIONS
|
More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 12 2009
|
|
|
Search completed in 0.002 seconds
|
