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A085480 Expansion of 3*x*(1+2*x)/(1-3*x-3*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 (list; graph; refs; listen; history; text; internal format)
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(n-1)+3*a(n-2), 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*k-3)/(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: A212869 A147618 A261565 * A265974 A099581 A026696

Adjacent sequences:  A085477 A085478 A085479 * A085481 A085482 A085483

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jul 02 2003

STATUS

approved

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Last modified March 23 20:30 EDT 2017. Contains 283957 sequences.