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43, 175, 395, 703, 1099, 1583, 2155, 2815, 3563, 4399, 5323, 6335, 7435, 8623, 9899, 11263, 12715, 14255, 15883, 17599, 19403, 21295, 23275, 25343, 27499, 29743, 32075, 34495, 37003, 39599, 42283, 45055, 47915, 50863, 53899, 57023, 60235
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OFFSET
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1,1
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COMMENTS
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The identity (44*n^2-1)^2-(484*n^2-22)*(2*n)^2 = 1 can be written as a(n)^2 - A158627(n)*A005843(n)^2 =1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: x*(-43-46*x+x^2)/(x-1)^3.
a(n)= 3*a(n-1) -3*a(n-2) +a(n-3).
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MATHEMATICA
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44Range[0, 40]^2-1 (* or *) CoefficientList[Series[(1-46 x-43 x^2)/ (x-1)^3, {x, 0, 40}], x] (* From Harvey P. Dale, Apr 22 2011 *)
LinearRecurrence[{3, -3, 1}, {43, 175, 395}, 40] (* Vincenzo Librandi, Feb 17 2012 *)
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PROG
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(MAGMA) I:=[43, 175, 395]; [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 17 2012
(PARI) for(n=1, 40, print1(44*n^2-1", ")); \\ Vincenzo Librandi, Feb 17 2012
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CROSSREFS
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Cf. A005843, A158627.
Sequence in context: A057816 A162295 A187722 * A123597 A138631 A142115
Adjacent sequences: A158625 A158626 A158627 * A158629 A158630 A158631
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 23 2009
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EXTENSIONS
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Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009
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STATUS
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approved
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