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A049682
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a(n)=(L(8n)-2)/45, where L=A000032 (the Lucas sequence).
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3
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0, 1, 49, 2304, 108241, 5085025, 238887936, 11222647969, 527225566609, 24768378982656, 1163586586618225, 54663801192073921, 2568035069440856064, 120642984462528161089, 5667652234669382715121, 266259012044998459449600, 12508505913880258211416081
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is a divisibility sequence.
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LINKS
| Index to divisibility sequences.
Index to sequences with linear recurrences with constant coefficients, signature (48,-48,1).
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FORMULA
| a(n) = (1/45)*{-2+[(47+7*sqrt(45))/2]^n+[(47-7*sqrt(45))/2]^n}. - R. Stephan, Apr 14 2004
a(n)=(A004187(n))^2 = 48*a(n-1)-48*a(n-2)+a(n-3). G.f.: -x*(1+x)/((x-1)*(x^2-47*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
a(n)=F(4n)^2/9. Also a(n) - a(n-1) = A004187(2n-1). - R. K. Guy, Feb 24 2010
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MATHEMATICA
| LinearRecurrence[{48, -48, 1}, {0, 1, 49}, 20] (* or *) CoefficientList[Series[ (-x-x^2)/ (x^3-48x^2+48x-1), {x, 0, 20}], x] (* From Harvey P. Dale, Apr 22 2011 *)
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PROG
| (Mupad) numlib::fibonacci(4*n)^2/9 $ n = 0..25; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
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CROSSREFS
| Sequence in context: A065785 A163927 A061615 * A162914 A163287 A163835
Adjacent sequences: A049679 A049680 A049681 * A049683 A049684 A049685
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from N. J. A. Sloane, Feb 26 2010
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