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A087287
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a(n) = Lucas(9*n).
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11
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2, 76, 5778, 439204, 33385282, 2537720636, 192900153618, 14662949395604, 1114577054219522, 84722519070079276, 6440026026380244498, 489526700523968661124, 37210469265847998489922, 2828485190904971853895196, 215002084978043708894524818, 16342986943522226847837781364, 1242282009792667284144565908482
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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 (76 + sqrt(5780))/2 = 76.01315561749...
a(0)/a(1) = 2/76, a(1)/a(2) = 76/5778, a(2)/a(3) = 5778/439204, a(3)/a(4) = 439204/33385282, etc.
Lim_{n->infinity} a(n)/a(n+1) = 0.01315561749... = 2/(76 + sqrt(5780)) = (sqrt(5780) - 76)/2.
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LINKS
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FORMULA
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a(n) = 76a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 76.
a(n) = ((76 + sqrt(5780))/2)^n + ((76 - sqrt(5780))/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) = 33385282 = 76*a(3) + a(2) = 76*439204 + 5778 = ((76 + sqrt(5780))/2)^4 + ((76 - sqrt(5780))/2)^4 = 33385281.999999970046... + 0.000000029953... = 33385282.
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MATHEMATICA
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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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