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A085480
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a(n) = p^n + q^n, where p = (3 + sqrt 21)/2, q = (3 - sqrt 21)/2.
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3
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| A Jacobsthal variation.
p - q = sqrt 21; pq = -3; p + q = 3.
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REFERENCES
| Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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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]
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EXAMPLE
| a(4) = q^4 + q^4 = 207; p^5 + q^5 = 783, where p = (3 + sqrt 21)/2, q = (3 - sqrt 21)/2.
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CROSSREFS
| Cf. A030195.
Sequence in context: A166035 A038192 A147618 * A099581 A026696 A082708
Adjacent sequences: A085477 A085478 A085479 * A085481 A085482 A085483
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 02 2003
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EXTENSIONS
| More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 12 2009
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