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A158556
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a(n) = 28*n^2 + 1.
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2
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1, 29, 113, 253, 449, 701, 1009, 1373, 1793, 2269, 2801, 3389, 4033, 4733, 5489, 6301, 7169, 8093, 9073, 10109, 11201, 12349, 13553, 14813, 16129, 17501, 18929, 20413, 21953, 23549, 25201, 26909, 28673, 30493, 32369, 34301, 36289, 38333, 40433, 42589, 44801, 47069
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OFFSET
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0,2
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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 a(n)^2 - A158555(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: (1 + 26*x + 29*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(28))*Pi/sqrt(28) + 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(28))*Pi/sqrt(28) + 1)/2. (End)
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MATHEMATICA
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PROG
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(Magma) I:=[1, 29, 113]; [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, Mar 02 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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