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A087281
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a(n) = Lucas(7*n).
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10
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2, 29, 843, 24476, 710647, 20633239, 599074578, 17393796001, 505019158607, 14662949395604, 425730551631123, 12360848946698171, 358890350005878082, 10420180999117162549, 302544139324403592003, 8784200221406821330636, 255044350560122222180447, 7405070366464951264563599
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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, ....
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EXAMPLE
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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
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LucasL[7Range[0, 20]] (* or *) LinearRecurrence[{29, 1}, {2, 29}, 20] (* Harvey P. Dale, Nov 22 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
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EXTENSIONS
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STATUS
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approved
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