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A158555
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a(n) = 196*n^2 + 14.
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2
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14, 210, 798, 1778, 3150, 4914, 7070, 9618, 12558, 15890, 19614, 23730, 28238, 33138, 38430, 44114, 50190, 56658, 63518, 70770, 78414, 86450, 94878, 103698, 112910, 122514, 132510, 142898, 153678, 164850, 176414, 188370, 200718, 213458, 226590, 240114, 254030
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OFFSET
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0,1
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COMMENTS
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The identity (28*n^2 + 1)^2 -(196*n^2 + 14)*(2*n)^2 = 1 can be written as A158556(n)^2 - a(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: 14*(1 + 12*x + 15*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(14))*Pi/sqrt(14) + 1)/28.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(14))*Pi/sqrt(14) + 1)/28. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {14, 210, 798}, 50] (* Vincenzo Librandi, Feb 05 2012 *)
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PROG
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(Magma) I:=[14, 210, 798]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // 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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