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A087281 a(n) = Lucas(7*n). 10
2, 29, 843, 24476, 710647, 20633239, 599074578, 17393796001, 505019158607, 14662949395604, 425730551631123, 12360848946698171, 358890350005878082, 10420180999117162549, 302544139324403592003, 8784200221406821330636, 255044350560122222180447, 7405070366464951264563599 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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_{n->infinity} a(n)/a(n+1) = 0.0344418537... = 2/(29+sqrt(845)) = (sqrt(845)-29)/2.
LINKS
Tanya Khovanova, Recursive Sequences
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). - Philippe Deléham, Nov 02 2008
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.
MATHEMATICA
LucasL[7Range[0, 20]] (* or *) LinearRecurrence[{29, 1}, {2, 29}, 20] (* Harvey P. Dale, Nov 22 2011 *)
PROG
(Magma) [ Lucas(7*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011
CROSSREFS
Cf. A000032.
Sequence in context: A282735 A245252 A090251 * A024234 A367551 A077282
KEYWORD
easy,nonn
AUTHOR
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
EXTENSIONS
More terms from Ray Chandler, Feb 14 2004
More terms from Vincenzo Librandi, Apr 14 2011
STATUS
approved

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Last modified July 23 16:21 EDT 2024. Contains 374552 sequences. (Running on oeis4.)