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A158628
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a(n)=44*n^2-1 (n>0)
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (44*n^2-1)^2 - (484*n^2-22)*(2*n)^2 = 1 can be written in
Pell-format as (a(n))^2 - A158627(n)* (A005843(n))^2 =1.
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LINKS
| Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
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FORMULA
| a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: x*(-43-46*x+x^2)/(x-1)^3.
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MATHEMATICA
| 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 *)
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CROSSREFS
| 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
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 23 2009
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EXTENSIONS
| Comment rewritten, formula replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2009
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