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A158540
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a(n) = 22*n^2 - 1.
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2
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21, 87, 197, 351, 549, 791, 1077, 1407, 1781, 2199, 2661, 3167, 3717, 4311, 4949, 5631, 6357, 7127, 7941, 8799, 9701, 10647, 11637, 12671, 13749, 14871, 16037, 17247, 18501, 19799, 21141, 22527, 23957, 25431, 26949, 28511, 30117, 31767, 33461, 35199, 36981, 38807
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OFFSET
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1,1
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COMMENTS
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The identity (22*n^2 - 1)^2 - (121*n^2 - 11)*(2*n)^2 = 1 can be written as a(n)^2 - A158539(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(-21 - 24*x + x^2)/(x-1)^3.
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(22))*Pi/sqrt(22))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(22))*Pi/sqrt(22) - 1)/2. (End)
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MATHEMATICA
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22Range[40]^2-1 (* or *) LinearRecurrence[{3, -3, 1}, {21, 87, 197}, 40]
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PROG
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MAGMA) I:=[21, 87, 197]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 14 2012
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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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EXTENSIONS
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STATUS
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approved
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