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Search: id:A158766
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| 38, 1482, 5814, 13034, 23142, 36138, 52022, 70794, 92454, 117002, 144438, 174762, 207974, 244074, 283062, 324938, 369702, 417354, 467894, 521322, 577638, 636842, 698934, 763914, 831782, 902538, 976182, 1052714, 1132134, 1214442, 1299638
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OFFSET
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0,1
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COMMENT
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The identity (76*n^2+1)^2 - (1444*n^2+38) * (2*n)^2 = 1 can be written as
the Pell equation (A158767(n))^2 - a(n) * (A005843(n))^2 = 1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: -38*(1+36*x+39*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158767
Sequence in context: A078987 A009982 A041685 this_sequence A093648 A055605 A096558
Adjacent sequences: A158763 A158764 A158765 this_sequence A158767 A158768 A158769
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 26 2009
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EXTENSIONS
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Comment rewritten, a(0) added, and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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