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Search: id:A014448
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| A014448 |
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Even Lucas numbers: L(3n). |
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+0
5
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| 2, 4, 18, 76, 322, 1364, 5778, 24476, 103682, 439204, 1860498, 7881196, 33385282, 141422324, 599074578, 2537720636, 10749957122, 45537549124, 192900153618, 817138163596, 3461452808002, 14662949395604, 62113250390418
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
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G.f.: (2-4*x)/(1-4*x-x^2); a(n)=4*a(n-1)+a(n-2), a(0)=2, a(1)=4; a(n)=(2+sqrt(5))^n + (2-sqrt(5))^n.
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PROGRAM
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(PARI) polsym(x^2-4*x-1, 100)
(Other) sage: [lucas_number2(n, 4, -1) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
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A001077(n)=A014448(n)/2. A014448(n)=A000032(3n).
Sequence in context: A007727 A052689 A139104 this_sequence A075836 A120664 A095816
Adjacent sequences: A014445 A014446 A014447 this_sequence A014449 A014450 A014451
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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