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A333718
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a(n) = L(8*n+4)/7, where L=A000032 (the Lucas sequence).
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1
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1, 46, 2161, 101521, 4769326, 224056801, 10525900321, 494493258286, 23230657239121, 1091346396980401, 51270050000839726, 2408601003642486721, 113152977121196036161, 5315781323692571212846, 249728569236429650967601, 11731926972788501024264401, 551150839151823118489459246
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OFFSET
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0,2
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COMMENTS
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a(n) is the denominator of the continued fraction [3*sqrt(5), 3*sqrt(5),..., 3*sqrt(5)] with 2n+1 terms.
a(n) = (2/7)*T(2*n+1, 7/2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Jul 08 2022
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LINKS
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FORMULA
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a(n) = 47*a(n-1) - a(n-2) for n>2.
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EXAMPLE
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The continued fraction [3*sqrt(5), 3*sqrt(5), 3*sqrt(5)] with 2*1 + 1 terms equals 141*sqrt(5)/46, and 46 is our a(1) term.
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MATHEMATICA
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Table[LucasL[8 n + 4]/7, {n, 0, 20}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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