

A085480


Expansion of 3*x*(1+2*x)/(13*x3*x^2).


3



3, 15, 54, 207, 783, 2970, 11259, 42687, 161838, 613575, 2326239, 8819442, 33437043, 126769455, 480619494, 1822166847, 6908359023, 26191577610, 99299809899, 376474162527, 1427321917278, 5411388239415, 20516130470079
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OFFSET

1,1


COMMENTS

A Jacobsthal variation.
p  q = sqrt 21; p*q = 3; p + q = 3.


REFERENCES

Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.


LINKS

Table of n, a(n) for n=1..23.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (3,3).


FORMULA

a(n) = p^n + q^n, where p = (3 + sqrt 21)/2, q = (3  sqrt 21)/2.
a(n)=3*a(n1)+3*a(n2), a(1)=3, a(2)=15. [From Philippe Deléham, Nov 19 2008]
G.f.: G(0)/x 2/x, where G(k)= 1 + 1/(1  x*(7*k3)/(x*(7*k+4)  2/G(k+1))); (continued fraction).  Sergei N. Gladkovskii, Jun 03 2013


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: A290764 A286986 A261565 * A265974 A099581 A026696
Adjacent sequences: A085477 A085478 A085479 * A085481 A085482 A085483


KEYWORD

nonn,easy


AUTHOR

Gary W. Adamson, Jul 02 2003


STATUS

approved



