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Search: id:A038762
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| A038762 |
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a(n)=6a(n-1)-a(n-2) for n >= 2, with a(0)=3, a(1)=13. |
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+0
3
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| 3, 13, 75, 437, 2547, 14845, 86523, 504293, 2939235, 17131117, 99847467, 581953685, 3391874643, 19769294173, 115223890395, 671574048197, 3914220398787, 22813748344525, 132968269668363, 774995869665653
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A Pellian-related sequence.
a(n)={13*([3+2*sqrt(2)]^n -[3-2*sqrt(2)]^n)-3*([3+2*sqrt(2)]^(n-1) - [3-2*sqrt(2)]^(n-1))}/(4*sqrt(2)).
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
M. J. DeLeon, Pell's Equation and Pell Number Triples, Fib. Quart., 14(1976), pp. 456-460.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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Equals sqrt{2*(A038761)^2+7}.
a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3); a(n) = (1/2)*(3+sqrt(2))*(3+2*sqrt(2))^(n-1)+(1/2)*(3-sqrt(2))*(3-2*sqrt(2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Apr 20 2008
G.f.: (3-x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
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CROSSREFS
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Cf. A038761.
a(n) = A077443(2n) = A038725(n)+A038725(n+1).
Sequence in context: A020094 A009382 A110193 this_sequence A074517 A007178 A034172
Adjacent sequences: A038759 A038760 A038761 this_sequence A038763 A038764 A038765
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 03 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 04 2000
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