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Search: id:A056914
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| A056914 |
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a(n)=L(4n+1) where L() are the Lucas numbers. |
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+0
1
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| 1, 11, 76, 521, 3571, 24476, 167761, 1149851, 7881196, 54018521, 370248451, 2537720636, 17393796001, 119218851371, 817138163596, 5600748293801, 38388099893011, 263115950957276, 1803423556807921, 12360848946698171
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers, A Publication of the Fibonacci Association, Houghton Mifflin Co., 1969, pps. 27-29.
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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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a(n)=7a(n-1)-a(n-2); a(0)=1, a(1)=11.
G.f.: (1-4*x)/(1-7*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(n)={11*[((7+3*sqrt(5))/2)^n - ((7-3*sqrt(5))/2)^n]-[((7+3*sqrt(5))/2)^(n-1) - ((7-3*sqrt(5))/2)^(n-1)]}/3*sqrt(5).
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CROSSREFS
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Cf. (A056914)=sqrt{5*(A033889)^2-4}.
Sequence in context: A036427 A122589 A034269 this_sequence A039674 A059625 A023010
Adjacent sequences: A056911 A056912 A056913 this_sequence A056915 A056916 A056917
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jul 11 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 13 2000
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