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A087281
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Lucas numbers L(7*n).
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0
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2, 29, 843, 24476, 710647, 20633239, 599074578, 17393796001, 505019158607, 14662949395604, 425730551631123, 12360848946698171, 358890350005878082, 10420180999117162549, 302544139324403592003, 8784200221406821330636, 255044350560122222180447, 7405070366464951264563599
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n+1)/a(n) converges to (29+sqrt(845))/2 = 29.0344418537... a(0)/a(1)=2/29; a(1)/a(2)=29/843; a(2)/a(3)=843/24476; a(3)/a(4)=24476/710647; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.0344418537... = 2/(29+sqrt(845)) = (sqrt(845)-29)/2.
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
| a(n) =29*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 29.
a(n) = ((29+sqrt(845))/2)^n + ((29-sqrt(845))/2)^n.
(a(n))^2 =a(2n)-2 for n=1, 3, 5..., (a(n))^2 =a(2n)+2 for n=2, 4, 6....
G.f.: (2-29*x)/(1-29*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
| a(4) = 710647 = 29*a(3) + a(2) = 29*24476+ 843=((29+sqrt(845))/2)^4 + ( (29-sqrt(845))/2)^4 =710646.9999985928 + 0.0000014071 = 710647.
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MATHEMATICA
| LucasL[7Range[0, 20]] (* or *) LinearRecurrence[{29, 1}, {2, 29}, 20] (* From Harvey P. Dale, Nov 22 2011 *)
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PROG
| (MAGMA) [ Lucas(7*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011
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CROSSREFS
| Cf. A000032.
Sequence in context: A176938 A006988 A090251 * A024234 A077282 A059725
Adjacent sequences: A087278 A087279 A087280 * A087282 A087283 A087284
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KEYWORD
| easy,nonn
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AUTHOR
| Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2004
More terms from Vincenzo Librandi, Apr 14 2011
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