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A158673
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a(n) = 60*n^2 + 1.
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3
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1, 61, 241, 541, 961, 1501, 2161, 2941, 3841, 4861, 6001, 7261, 8641, 10141, 11761, 13501, 15361, 17341, 19441, 21661, 24001, 26461, 29041, 31741, 34561, 37501, 40561, 43741, 47041, 50461, 54001, 57661, 61441, 65341, 69361, 73501, 77761, 82141, 86641, 91261, 96001
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OFFSET
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0,2
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COMMENTS
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The identity (60*n^2+1)^2 - (900*n^2+30)*(2*n)^2 = 1 can be written as a(n)^2 - A158672(n)*A005843(n)^2 = 1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
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FORMULA
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G.f.: (1+58*x+61*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/(2*sqrt(15)))*Pi/(2*sqrt(15)) + 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/(2*sqrt(15)))*Pi/(2*sqrt(15)) + 1)/2. (End)
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MATHEMATICA
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PROG
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(Magma) I:=[1, 61, 241]; [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 19 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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Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009
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STATUS
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approved
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